I really like the lighter feel and the more comfortable grip of the 6D. I returned my D600 due to dust problems... I have been a Canon G series user for YEARS and loved all of them. In film days I used Nikon,,, F2s & F3s.
The D600 was uncomfortable but I lied the DR and IQ.
How do the 6D users here like the camera?
I do fine Art, Street photography and landscapes.
I currently still have a D600 + a EOS6D + a D800E and a couple of 5DMK2 bodies,which will be replaced by the 5D3 soon.
1 DR at base ISO the D600 wins , but not as significantly different as DXO or many moronic test chart only shooters making it out to be, it is just a stop or a stop and half difference, and not really dramatic.
2 high ISO , the 6D is a stop better , with better DR from ISO 800.
3 video , the 6D is better and it will get ML RAW , so it will be much better , not just a bit better.
4 size and weight , the 6 D is actually quite significantly smaller but not much lighter(I love the 6D +35mm f2IS, and I consider that as an ultimate lowlight kit).
5 battery life , the D600 wins hands down here.
6 the D600 has better dual SD card slots, the 6D has just one slot (this is a big deal if you need a back up slot all the time for wedding)
7 the 6 D can focus in real lowlight rated down to -3 EV, which is really dim , as dark as moon light level , but the D600 tracks moving things a bit better.
8 Wifi is a big thing , you can control the camera remotely while shooting long exposure or any kind of tripod based work.
9 the D600 has crappy pop-up flash and I think that makes it look cheap and actually it does break easily. my D700 had really annoying pop-up flash related issues, and I had to send it in for service 7 times and I finally sold it for the 5D2. the D600 seems even weaker than my D700 or 800E. so I expect it to be quite fragile.
10 IMO, the 6D built better with a bit more comfortable grip, but it is subjective , for me the A99V is the most comfortable camera to shoot with , its grip was as though it had been designed specifically for my right hand.
the 5D3 was the second most comfortable camera to hold and shoot with.
11 AWB is very very different , the Nikon has a bit of Cyan cast in it , while the Canon has a bit of Magenta cast in it.
12 There are almost no zooms that can resolve the 24.3 mp FX sensor well in current Nikon zoom line (maybe the 70-200VR2 and 200-400f4VR2 are fine), so if you are zoom shooter , you are wasting much potential resolving power of the high resolution sensor of the Nikon. I , in fact , recommend Zeiss primes and 70-200mmf2.8VR2 for the Nikon , nothing less than that is really good enough for that sensor. the Nikon 24-70mmf2.8G ED , 16-35mmf4VR , 24-120mmf4VR, the 70-200f4GEDVR are all useless , they were great on 12mp generation bodies but not on the D800E or D600.
So , I think you should go down to a local shop and just try the 6D , 5D3 , A99v ,etc and see which one fits best in your right hand.
They are all good but not perfect or objectively better than the others , so just try them all and decide it for yourself. do not listen to others including me and people here since all of us are biased , even DXO is biased towards Nikon /Pentax ,etc.
Finally, one thing I am sure about by now is 36mp vs 24 is not that big difference in real life use, but usable aperture sweet spot gets much narrower with the 36mp sensor due to diffraction effect.
In order to get best out of it , we really need focus stacking and stitching in PS all the time ,so unless going at least 48mp or a bit more , it is meaningless to up the resolution from 20mp -24mp range, you will need to stitch or focus stack anyway(as you want to get best out of it).