Thank you AmbientLight for your kind advice. I think you are right about FF since I was having a lot of trouble with the 7D obtaining focus and also keeping the whole bird in the frame. One day I hope to upgrade to the 5D3 or something similar in the future.
What lens are you using? I use a 70-300L with a 7D for birds in flight and would just use less zoom than buy a new full frame body. The auto focus of the 7D is more than adequate for sharp birds in flight when used with a fast enough shutter speed. If birds are flying laterally, it's hard to get a high percentage of keepers, but with the 7D's frames/second, you should get some. Do you use back button focus in servo? That change helped my "keep" rate a lot.