I did the same thing, went to a 5d3 from a 1d4, and after a couple of seasons in sports, the 5d3 has done everything as well as the 1d4, and better regarding iso. I have now added a 7d2 to the mix.
I too have the 5d3 and the 7d2. I bought the 5 to supplement my 7d1, mainly to get better quality on landscapes. I then sold the 7d and bought a 7d2. I suspect that GAS intervened, as the majority of my shooting is now birds and wildlife and the 7d2 has become the go to body due to the perceived effective extra reach and the 5d3 gets less use. I probably could have saved some money and not bought the 5d3. The Sigma 120 - 300 f/2.8 + TCs might then have been a 500 or 600 f/4 or 200 - 400. As I almost almost always have the 2x installed with the with the Sigma this might have been the better option.
Having said that, the AF and noise profile for the 5d3 were much better than the 7D1 and having 2 bodies allows me to have both long and wide lenses in play. Plus, I also have a backup body.
I don't think I would swap my 2 bodies for a single 1 series now, however the 1D4 might have been a good option for me a couple of years ago. My next purchase is likely to be lens rather than body, if I can persuade the better half that it is a good idea. Plenty of jewellery might help. (As she makes jewellery as a hobby, this isn't as expensive as it might sound, although I am sure a few pearls or amethysts is worth a 600 f/4 ߙ.
This has been a much much longer and more rambling post than I intended, probably due to the (now empty) bottle of Australian red on the table. Since my company sent me from Scotland to Australia for a trip I thought it was only fair.