The real advantage over the 5D II is only the Autofocus..and yet not complete!!!
Better High ISO, better layout/ergonomics, better AFMA, better grip, better video (I can't honestly comment on this as I have never shot video with any DSLR), Nice having an extra card slot just in case (should have been a CF card!), better high end card performance (if that matters to you), The AF on the Mk3 blows the Mk2 out of the water, better NR, better processor and I feel a much better overall build.
... and to add to that: more responsive shutter, shorter mirror blackout, 100% viewfinder, two amazing quiet shutter modes, good implementation of auto-ISO, better auto white balance, higher frame rate, etc. So, the hugely improved autofocus is definitely NOT the "only" real advantage.
I agree with Mt Spokane who writes that the "grass is not greener". Look at the current star ratings on Amazon.com:
D800: 42 out of 239 are 1 star (worst) ratings = 17.5%
D600: 40 out 225 are 1 star (worst) ratings = 17.7%
5D3: 4 out of 201 are 1 star (worst) ratings = 2%
6D: 0 out of 58 are 1 star (worst) ratings = 0%
Based on specs on paper, those Nikon models should be providing greater value. But based on customer ratings, they are providing greater dissatisfaction.
Very very good points. I forgot about quiet shutter which I have to say is amazing.
Quiet shutter - works really well at weddings 
I think I forgot because I can hardly hear it at events like that=)
+1
Don't forget that the auto-focus of the 5D III is not all the same as 1D x's,
while that seems no big difference, it surely is a lot better in low light,
without mentioning the spot-meter linked to all AF points.
Even the 6D's center AF point is better in low light than 5D III's any AF Point
So, the 5D III IS a lot better camera than its predecessor, there still are
some important limitations even for weddings or low light events.
I've had troubles achieving a good focus with all the lenses in some
low light situations.
I don't know what will the next 5D camera have or improve,
but i think there's still room of improving the auto-focus.
We really didn't need all those AF points,
nor should it have all that ''complicated'' auto-focus,
All it should have was a 1Dx-like low light performance with fewer AF points
Anyway it's just my opinion