OK so I"m lucky enough to have the EM5-II with 12-40mm f2.8 (as well as the 45mm f1.8 and 40-150mm R) and the D750 with various lenses which are similar enough to give an idea of the EM1 vs D610, or in the case of Liyama the Em1 vs D750.
In some situations it is extremely hard/nigh on impossible to tell the difference in IQ between the EM5-II and D750. Such an example is in the studio. I got invited to both a Nikon and Olympus Studio lighting classes last year and I really can't tell the difference. OK so I wasn't using comparative lenses, one being a prime (the £180 45mm f1.8 Olympus) and one a pro zoom (the £1500 70-200mm f2.8 VRII Nikon) but if you look at it on price alone the Nikon should be significantly better but as I said already I can't see any difference in sharpness or detail.
In the 'real world' things are a little different. At base ISO's again there's not a lot to split them. OK for landscapes the dynamic range of the D750 helps a lot, and the recovery in PP on the D750 is ridiculous, especially the shadow recovery. Also, overall I would say that the D750 has more pop and depth to an image, but this of course depends on subject matter etc and sometimes it's very subtle. Start ramping up ISO and the difference becomes more significant. There's the obvious noise differences but the 'pop'/depth of the image difference widens too. I find at higher ISO's (1600+) the EM5-II images start to look a bit flat.
Auto WB and metering of the D750 is significantly better, I don't know how they do it but I can leave it in Auto WB and wide/matrix metering 99% of the time and it gets it right. Autofocus is another area where the D750 excels over the EM5-II. In S-AF the EM5-II is mega quick, but the D750 is quicker and more consistent. In C-AF there's no comparison, absolute night and day. AF in low light, again no comparison, the D750 can see in the dark.
Overall I find the controls of the D750 better, and it's quicker to access everything such as changing metering modes, AF modes etc. (one hint is to set the record button as ISO as it makes changing ISO much quicker)
One huge advantage of the EM5-II is the IBIS, the best IS of any kind I've used, truly remarkable. I can handhold at 40mm (80mm eq) at 1s. The other advantage of the EM5-II is AF in liveview (using rear screen) is just as quick as the viewfinder, AF in liveview on the D750 is painfully slow.
The EM5-II is a truly great camera, and exceptional camera in fact, but I always choose to use the D750 as it's that much better.
As for the D610 vs D750, well the sensor is the same so performance and PP recovery etc should be the same. The AF spread on he D610 is quite small which can be an issue. AF spread on FF is small anyway, and can be limiting on occasion on the D750 so is even more limiting on the D610. Also the D750 has 51 AF points with 15 cross type vs 39 AF points and 9 cross type on the D610. The grip on the D750 is much nicer imo (at the expense of a smaller top LCD display), and the flip screen on the D750 comes in very handy for landscapes especially. So is the D750 worth £300 more than the D610? Only the individual can decide. For me though it's a resounding yes.
TBH I use my Olly so little I'm probably going to put it up for sale this weekend. I'm just going to by a high end compact for those times I absolutely don't want to be carrying any bulk, for the rest of the time I'd rather put up with the weight and use my D750.