As some of the guys already said - Nikon or Canon cannot be answered easily. I think it is safe to say that except for the very cheapest models, cameras from both makes will produce very nice images, with small differences. IMHO you have to look what is the best camera for the type of photography you want to do. Or at the price range you're aiming for, and then see which of the two makes the better camera for the amount of money you want to spend.
I would rely more comparing specs and reading reviews, and maybe even trying the camera at the store, than on a generalising statement which brand is better. And not to forget - there are other companies which make great cameras too. In the price range of the 500D, why not look at micro four thirds? They do have advantages, like size and some also have interesting operating concepts, and their image quality may be perfectly good enough for what you want.
That said, I switched from Canon to Nikon (a D800 currently) last year, but not because Nikon is better, but because the D800 has features which are good for the type of pictures I want to shoot. If I were into shooting moving people or even sports, I'd have a Canon, because they offer better priced cameras which are good for those categories. Or even an Olympus OMD E-M1, which features a max shutter speed of 1/16000 (although snapsort says otherwise).
That new camera has given me better pictures, but not because 'Nikon is better', but for one because this particular camera has a very high dynamic range and color depth and I often take pictures which require this, and secondly because I spend a lot of time thinking and preparing the pictures, so I actually try to use the camera properly and make the best use of what it can do.
For other purposes, a Canon may be better. I think Nikon has the technically more advanced sensors in the midrange cameras like the D800, but the sensors are not the only important criterion. If for example you'd like to spend around 1300 GBP, you'd be looking at Canon 6D and Nikon D610. There, the D610 offers more top end features than the 6D, so in this price segment, the Nikon would be my personal choice. If I wanted to spend 500 GBP, you might opt for the technically more advanced sensor, but maybe you like the image processor of the Canon better, because the processor and software are also an important in what the images look like.
I've been saying the above not to give an exhaustive overview of features to consider, but to point out that the question you asked cannot be answered in a general way. You always have to consider what you want to do, and then find the right camera for that purpose.
As for what others above said about improving technique, I think most of us have to humbly concede, we all need to try and improve out technique, giving more thought to composition and settings. But OTOH, if someone asks about cameras, why not reply to the question instead of lecturing - after all, the person asking may be very aware of that aspect and ask the question regarding the camera for a good reason.
. If you're upgrading then think about your options too, do you go from a crop frame to full-frame, or just go for crop-frame but better spec?
