I had thought you already bought a 5D3 and were using it with your 600 ii. Would drive me nuts I think!
I have used "a" 5D III with my 600 II, but I have not yet purchased a 5D III of my own yet. I can only absorb so much outflow in a year, and the lens sucked me dry. So...5D III is on hold until I have more cash flow and savings.
The slight jitter that causes those misses is also present in the 7D's 19pt AF system...it just doesn't sit still between shots...even if the subject is already locked, there is pretty much ALWAYS movement, ever so slight, between every frame.
Of what mode are you talking about - servo af or one-shot with continuous fps?
What I experience on both the 6d and 60d with a thinner dof like on the 100L is that when you re-af at the same point w/o camera movement, the lens will often choose a slightly different focus... and lensrentals says it's even better to af somewhere completely else first as this gives more exact results than slight af corrections.
Either, in the case of the 7D, but it is more pronounced with Servo. This isn't a DOF problem. It happens with all my lenses, wide open or stopped down considerably. I had the problem with my 600/4II when stopped down to f/8 just the other day. For such a long lens like that, DOF is pretty small when you get close enough to a bird to be "frame filling", and even at f/8, the jitter can still result in slight softening of detail that isn't exactly at the plane of focus. I like the 7D, but the AF jitter is the single largest IQ drawback of the camera.
All of my lens are properly AFMAed as well. I've used manual techniques as well as FoCal to calibrate each of my lenses. Even shifting AFMA about 2-3 notches results in a visible change with the 600mm lens, so when the lens is that sharp, slight changes in the focal plane can mean visible changes elsewhere, unless you are downsampling by 2x or more. (When downsampling, it is never really a problem, but I generally print 24x36 and larger, so it really matters.)
For filling the frame with a bird at 600mm on the 7D, I could definitely see how even slightly closed to f/8, the plane of focus is extremely shallow, and thus your autofocus will vary on what it focuses on, and with the accuracy of that focus. You're usually trying to get the eye of the bird in sharpest focus, I assume? Plumage is important too, but less so than the eye, isn't it?
An APS-C at f/8 will have a deeper DOF than FF at f/8, for an identically framed subject. So in that sense, APS-C is actually better for DOF. The problem is most definitely not the depth of field, though...the 7D AF system has an uncontrolled jitter, such that it always adjusts every inter-frame period, even if it does not need to. For a stationary subject at a good distance with plenty of DOF, the actual plane of focus WILL shift around your intended focus point if you simply hold the AF button down and let it do it's thing. After a while, it will settle, so long as you do not take a picture. When you are doing AI servo and tracking a subject or taking multiple frames in sequence, ever frame the camera will perform AF, and even if the subject has not moved, the plane of focus will change...ever so slightly, but often just enough to be noticeable and sometimes enough to kill that frame.
However, if you're not filling the frame with a bird...like say especially if the bird is 1/4 the width of the frame or smaller, then in my opinion most of any focus problem, however minute, is easier to deal with and identify the cause. I guess that's obvious.
Hmm, not sure I understand... The smaller the bird is in the frame, the more pronounced any issue is, including missfocus...the fewer pixels you have on subject, the more magnified things like missfocus, camera shake, optical aberrations, etc. will be, relative to the subject.
In my opinion you can get pro quality images of birds by only filling the frame where the bird is a max of 1/3 the width (or height) of the image, but admittedly I'm not the birding expert. I've seen plenty of great images that were cropped about this much, though.
It really depends on the number of pixels in the area of the frame filled. The pros I follow generally fill the frame exactly right, regardless of the sensor used.