I upgraded from 7D to 6D. I also have shot with a friends 5D3 at sporting events.
If sports are your key focus, I found the 7D and 5D3's auto-focus to have a similar keeper rate. The 5D3s is better, but it didn't effect my photography substantially. Losing the crop advantage was sure noticed though.
I'm taking my 6D to shoot animals soon, I'm renting a 300mm to get the length back. The 7D with 70-200mm gave me a length of 320mm effectively.
If you need the length from your lenses, you may want to keep the 7D, and go with a 6D for other shoots, but if you don't need the length, then I'd go 5D3. I decided that I'm saving up for the 7D2 to pair with my 6D for lens reach reasons.
My friend who shoots birds professionally isn't upgrading his 1D4 because he doesn't want to lose the 1.3x crop either.
I have been somewhat debating the same issue. I have a 7D and it works well for what I do most which is sports - however, I have wanted to get a FF camera.
So for me, the question is do I sell the 7D and get a 5DIII, or keep the 7D for sports and get the 6D for most everything else.
I'm going to wait and see if a 7DII gets announced as a 6D & 7DII combo might be better than a 5DIII (which my current thinking is the 5DIII would be better than the 6D & 7D).
Until then, I'm happy with my 7D.