I can only echo what Ed said. I use my 400mm in Av mode, AI Servo and centre point focus. Also the lens is very sharp wide open so f5.6 presents no problems whatsoever and it keeps/gets the speed up especially of birds in flight on a sunny day.
I have never used the 300mm lens but I can assure you there is still more to come from the 400mm although your second bunch of shots are streets ahead of the first bunch. No offence intended.
I could post a couple of shots but fear it may hi-jack your thread, not that they are that good, and subsequent advice you may get.
A little bit of practice mate and you will be flying !
I do most of my birds in flight high up in the sky, so your advice makes perfect sense 


