Photography is all about catching light.
Here-in lies the dilemah of live-music photography, because the performances are often in the near-dark.. with harsh spot-lights illuminating very small 'bits' of the scene, worse still, them spot-lights is often coloured and turned on and off at the mixing desc.
The situation then makes it a much more challenging situation to get a decent photo in, before you start, and this fundamental 'problem' of the lack of light and inconsistent and peculiar light can give ANY camera a hard time...
Outdoors, on a typical sunny day, you have ambient sunlight, which is pretty consistent and gives rise to a thing called the f-16 Sunny Rule (of thumb). This says that the brightness of the light is 'about' enough to give you a 'good' exposure, for a shutter-speed one over the film/ISO number, at an aperture of f-16... which takes us into that murky world of 'Camera Settings' mentioning that alien 'jargon' you say you haven't come accross until today... and gives us a base line for how much of a raw beginner you are, but still... THIS is fundamental to the topic. As said, outdoors in good day-light, F-16-Sunny-Rule, suggests 'settings' of ISO100, the sensor-sensitivity, A shutter-Speed then of 1/100th of a second, at an aperture of f16... guide goes on, that as the sky gets cloudy or dark, you meed to adjust the 'exposure' and open the aperture or use a slower shutter speed; and when it used to be printed on boxes of film, suggested that after perhaps three or four 'stops' more exposure, you were indoors or in the dark, and to use 'flash'!
The Aperture is the size of a hole in the lens that lets light into the camera; bigger the hole, the more light it will let in, and the f-no is confusingly a ratio of hole diameter to the lens' focal length, so the f-number actually gets smaller as the hole gets bigger.... it also controls a thing known as Depth-of-Field, and the lower the f-number, so the shorter the distance around where the lens is focused you get 'in' focus... the scene starts to go blurry infront and behind the DoF zone.
The Shutter-Speed... how long the film or sensor is allowed light through the lens. Longer the shutter-speed, more light you get, but more likely that during that time the shutter is 'open' things are likely to move... like the camera, or the subject, or especially in live-gig photography, lights are likely to get switched on or off, and so your photo is likely to get blurred....
The ISO Is the sensor sensitivity. The 'native' sensitivity of the sensor is usually something around ISO100, and the ISO 'setting' you have on the camera, is the amount of electric amplification that the sensor signal is given, before the cameras electrickery look at the levels and 'paint by numbers' creating a table of data from the sensor data.
These things are important, and they are fundamental; and if you dont know what they are, or what they do, then jumping in trying NOT to get to grips with them, insisting you 'just' want to know what camera to buy, is like asking what aeroplane to buy, without learning to fly, or wanting to know what an aileron does.... Learn to fly, and you will probably have enough know-how to guess what sort of plane might be more of less suitable.... dont... well, you will probably crash anything at some point! So!
For starters, looking at your photo vs your mates. First up, yours is blurry... the subject on stage is rather more blurry than the back of the chap's head right infront of you..... this sort of suggests that the camera was focused on the 'near' subject, and the Depth of Field was rather shallow... probably trying to use a large aperture to let in as much light as it could from the dim scene. Next... the bloke on stage is blurry, and the beams of stage light look a bit 'smeared'. Suggests that the shutter-speed was also a tad 'low', also to let in more light from dim scene. Your mates picture? First of all, its a much tighter crop on the Drummer; he's used a lot more 'zoom'. This could be the lens, but on a camera-phone more likely digital-zoom, cropping a 'section' from the full scene the sensor sees. Fact it looks like the picture has been taken through a net-curtain and is rather pixilated, sort of supports this idea... but hey, the chap is in focus and not 'too' blury round the edges. ~So, the camera was focused more accurately on the subject, and whatever DoF the aperture gave better placed around him, and the shutter speed was likely a bit higher to not streak him or the stage-lights.....
Now, you like your mates shot 'better'... is that because it shows the drummer more starkly? If so that's simply because its a closer crop around the subject, not the whole stage. Your shot, fuzzy as it is, does show the 'atmosphere' of the event.... the blurryness conveys movement, the extra area around the performers, even the chaps head infront of you, provide context, of where you are and what you were at.
THINK about this....your mate's shot of the drummer, shows ONLY the drummer... you want picture of chap in a vest? Could have been taken in the bathroom, without anything else in the picture, he could be washing the dishes! It does NOT tell me, the viewer, what was going on, or why THAT photo is worth anything/
YOUR shot... yeah, I cant see the drummer, or for that matter, any-one elces face. Do I want to? Those stage lights, raking through the smog; its colorful, its obviously NOT a bathroom or kitchen, it IS a performance stage; I get that 'sense' straight away; yes the performers a blury... so what, they are moving, shows they were moving, I get more 'sense' of whats going on and the fact they were doing something, more still, there's a Forrest of folk infront of them, HEY! They were at a gog! ~A REAL gig, and it was BOPPING!
NOW... which is REALLY the 'better' photo?
It REALLY depends upon your point of view, BUT, your smudgy little effort ISN'T bad!!!! Its an honest snap-shot, capturing so much more of the event... your mates? Yeah, its bigger, its a tad clearer what the obviouse subject is... BUT, it doesn't capture ANY of the 'mood' or the 'event'.. and as a portrait? If you set out to get a photo of chap in his vest doing something with his hands beneath his waste... err... Oh-Kay... may be 'sharper'... but it's still not exactly a 'good' photo.....
HERE IN LIES THE LESSON!!
Good Photographers make good photo's NOT expensive cameras
And back to that f-16-sunny rule-of-thumb; at a gig, ANY camera is going to be struggling, SIMPLY from the lack of light in that situation, and the fact that things are likely to move and change, fairly fast...
Little Rock 'in-joke' Forkbeared's photo is of the Basist.... they DONT move as a rule, and I think it IS a rule, basists dont move.... they stand at the side of the stage and keep'd'beat-ma-a-n, whilst the lead guitarist plays to the crowd, and the drummer goes all animal with the sticks..... so he was onto a likely winner with his subject from the start! lol! But, again, its a tight crop, there's not a lot else in the picture, it could be during a performance, it could have been at a sound-test, showing noting else, it doesn't convey any 'mood' or dynamism of a live stage act... its just the Basist.... like your mate's shot of the drummer, it needn't have been at a gig or during a live performance.
THIS is where the shift starts; knowing what you want, and whether you want to achieve nice detailed portraits of the band.... in which case, is trying to get them when they are on stage during a performance REALLY the best way about it?
If you want a really good 'portrait' of a drummer; take them in a studio, give them a drum kit, and light them exactly how you want with studio stacks, and flash, and as much light as you need or want..... you DONT have to work under changing lighting of disco lights!
On stage, during a performance, ironically its everything and anything BUT the performer, that 'makes' that a photo worth taking...... and first thing 'cropped' out of almost every-one's gig shots, the clue to it being a 'live' performance not a studio-stages shot... the audience.... back of that chaps head in your picture! Its NOT a bit of distracting 'clutter', its real genuine 'context'...
And that's the leap twixt snapper and photographer; long before making decission over what camera-phone or proppa camera to buy, its the decision over what kind of photo you want to take.
THEN... having decided what kind of photo... what's the best way to get it? Like I say, you want nice neat portraits of a drummer, take them in a studio, use lighting stacks, pose them like you would a model in lingerie.... (hint, if working with a real drummer.... DONT take a model in real lingerie into the studio at the same time... well, not if you want a 'portrait'... you'd probably be able to sell the photo's to half a dozen web-sites otherwise... {the more observant might have noted I didn't say a 'woman' in lingerie.... more Rock-in-jokes as to how fussy drummer's tend to be!!! lol}) b--u--t like I say, first decision is what kind of picture you want!..
If you are going to take photo's of a 'live' performance, then it's that dynamism of the live show you are best able to capture, the 'mood' of the show; which means the odd bit of audience, to show its a real, live performance not a studio shot; NOT using so much 'zoom' to crop out all the 'context', and yes, a bit of 'fizzyness' blurring drum-sticks and stuff, can show the movement, can show that the performers are performing, they dont 'need' to be clinically 'sharp'.. and actually NOT being clinically sharp, and not being so close cropped, CAN be what makes live performance photo's stand out.
And then more.... know the performers. Bassists should just stand there; Drummers should be a blurr or Animal (muppets BTW) drum sticks and symbols; front of stage singer and lead guitarist aught be playing to the crowd..... and they oft have their own gimmics and moves.... go watch a Chuck Berry vid on You-Tube, see him doing his diddy-man strut, or Hendrix playing the gutar behind his back... THIS is the sort of thing that you get in a performance, that is a 'feature' that makes a photo... again, could be staged in a Studio, so go get the context. with it, BUT, this is the art of the job, and a lot of of it knowiung what the performers will do on stage, and what you want to get...
And its standard basic photo technique that will get it... knowing your subject... likely to mean going watch them 'live' a couple of times, to know what they will likely do worth snapping, when they will likely do it, and where to be to get the best angle on that action.....
THIS is little different to ANY photo-genre, whether its bird-spotting, or motor-sport or children's parties.... its about knowing your subject, and knowing what you want.
THE CAMERA matters little.
If you know your subject, if you know what you want to achieve, you will get it! ALL the camera can do is give you a few extra options, when its up against the buffers... and as said, gig-photo, you are up against the limits from the start, usually just because of low light.... BUT, a fancy camera wont make more light... might have a bigger flash....but debateable whether you want to chuck that into a lice performance, and blind the performers and anoy the audience, and NOT get what you see on stage... but something like they have turned the house-lights 'on'.... so its working with your kit, and knowing what the limits of your kit are.....
Here fancier cameras can, and I say 'can' it is only a potential, help you out a bit. You want to freeze motion, you want a faster shutter-speed, that means you need a larger aperture and or higher ISO.. but fancier cameras with bigger apertures and higher ISO settings WONT put you where the best angle to get a shot is; they wont know when the lead guitarist is going to start sliding accros the stage on thier back between the lead singers legs, they aren't going to know when the spot-light is going to rake accross the audience and blind you and the camera..... THIS is where YOU as photographer HAVE to start applying some craft, and not just scavenging scenes hoping that 'something' good will happen infront of you, and by serendipity, that the camera, will by chance grab it for you.....
A-N-D... USE LESS ZOOM!
Getting in tight, yeah, it gives a big in the frame 'obvious' subject, like your drummer.... but, it cuts out context in the doing, and its so often that context that 'makes' the photo.,.. like I said, its a matter of perspective whether you think your mates photo is any 'better' than yours... personally, I really don't think so... yeah, its sharper.. so what? Its a chap in a T-Shirt... could be in his bathroom doing dishes, its NOT obviously a drummer, during a lve show, or capturing any of the 'mood' of that show... which YOUR photo actually does.....
As to what camera? It's not the solution to the real problem. ANY camera, in the situation of a live performance is likely to struggle, and you will be up against the buffers of where the camera might help, vis having higher ISO's to be able to keep the shutter-speed up, having wider apertures to let in more light, but shrink DoF.... It just changes the 'mix' and shifts the inherent compromises you have to make, and without the know-how, without the 'craft' they wont make much odds either way.
Go back, critique yours and your mates photo's again, and try to look beyond how much 'bigger' the drummer is in his shot, and consider how much more 'mood' and 'atmosphere' you have captured; how they are very different shots. And ponder whether you want nice sharp photo's of chaps in vests.... or pictures of a live gig.. then what you need to get the photo's you want.... it's probably NOT to be got with a different camera.