Bird in flight with 5dMarkIII vs. 7D

Question for all you BIF fans. When I was using my 7D with the 100-400 mm f/4.5-5.6L IS USM, I was taking relatively great shots of the hawks that hang around in the canyon behind my house. I sold that and got the 5dMk III and I have never been able, even with cropping, to get the same quality of sharpness. I’m assuming it’s all technique but I’d like your opinions. I typically hand held the 7D at 1/1250 in good light. The hawks are usually gliding on the thermals and not fast. The 5dIII is perfect for me otherwise. The discussion about FF and crop bodies reminded me about this and why I’m bringing it up. I just saw someone else with the same sort of query. Any ideas or suggestions would be appreciated.