5D3 hands down. Superb AF and high-iso performance are much more important than "reach" IMO. In the end most likely you will end up cropping your pics regardless what body you use. Besides 5D3 has much better IQ than 7D.
I used to have 7d then upgraded to 1d4 and later acquired 5d3. I owned both 5d3 and 1d4 for a while and sold 1d4 because it's just sitting collecting dust. The IQ of 5D3 is just hard to beat and for me 6fps is all I need. The most important thing is learn the birds behavior, and try to get to birds as close as possible. Most of my bird pics were shot using 5D3. You will benefit "the reach" from crop body if you shoot mostly static-non moving birds, but if you shoot BIF, it's useless, you just cant predict where it comes or goes. It can be really far, which even using 1.6x crop body will not help or coming really close.
The reason you need high iso performance is because sometimes you have to go inside the woods where light is limited or when the weather is ugly. If necessary I would use iso 10000 and up and still get good quality pics, something I would never do with 7D.
Some samples using 5d3 and 300mm 2.8L IS II bare lens and not so much cropping, because those birds were pretty close to me.

Angry Birds

Swallow in Flight
5D3 & 28-300mm @300mm bare lens

Red Winged Blackbird
5D3 & 70-200mm @ 200mm bare lens

Bald Eagle, Vancouver, BC
Thanks 2loose, I agree, I love the IQ on the 5D MkIII, but my lens reach is pretty poor. What lens are you shooting with? Gorgeous shots, I will have to go look for you on Facebook or G+. 


