Your FZ50 has a very large depth of field compared to micro four thirds at the equivalent focal length and same aperture. So you think you have nailed the focus because it is good enough, even though you probably have actually often got focus on something behind your bird.
You're wrong. When you shoot at 714mm F3.7, even with a small sensor camera, DOF is tiny unless the bird is very far away. For example, if the bird is at 5 meters (not far from the minimum focus distance at those FL for the FZ50), the DOF is 4.8cm. So with only 2.4cm of far focus, you clearly see when it focuses on the branches behind, of course.
You seem to be far less picky than me in this regard...
It's a CDAF issue. PDAF is significantly better in this regard. It just is, I'm not giving an opinion, it's an observation that you can share by pixel-peeping away with the zillions of photos posted by various folk on the internet.
Among these photos, 24000 I took with the FZ50, and 67000 I took with E3+E5, and you can check more than 2400 here (with both systems), only about birds:
http://luis.impa.br/foto/birdindex.html
I assure you that the FZ50 CDAF is
far more more reliable than both the E3 and E5 PDAF for birds between branches,
if you use macro AF. Could I have too bad sample cameras of different models with exactly the same problem? Possible, but highly unlikely. Specially because AF is the Achilles heel of Olympus 43rds: many Oly users that switched systems did so precisely because of the unreliable AF.
BTW, have you tested macro AF in the FZ50? It works like magic, slowly though.
I'm sorry to hear you have had two bad Oly DSLR bodies and it would be something that would make me look elsewhere. I have had my E3 for three years and taken many thousands of photographs and the focus is consistently perfect, bad light, good light and particularly in the context we are talking about here. I can put a small focus point on a birds head and it will be in focus within a fraction of a second. Every time, with either the 50-200 or 12-60.
I would say again that perhaps you're less picky than me w.r.t. AF... OTOH, perhaps it is not pickyness: with identical conditions, at 200 vs 283 or 400 mm, your DOF is considerably bigger than mine, your subject is smaller, and hence critical focus is harder to check.
I have no intention of posting examples. It's a waste of time.
Thanks.
The difference your 1.4 teleconverter makes is incremental only.
Well, it's 'only' 41% bigger...

I wouldn't call that incremental. 400mm would useless for my uses, and 563mm EFL, although far from being good enough, is considerably better. And don't forget that I also have the EC20, so we're also comparing 400 vs 800mm. I wouldn't call that incremental either.
You still have to get very close to small birds and quite close to larger ones or you will end up with poor images regardless.
You always need to be as close as possible, of course. But 400mm is way too short for shooting small birds
in the wild . Of course for captive animals, all this discussion is totally irrelevant. You have plenty of time and short distance to take fantastic pictures of any subject... with any camera and any lens.
Cheers,
L.
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My gallery:
http://luis.impa.br/photos
Oly E5 + E3 + 12-60 + 50-200 + EC14 + FL50R
Pany FZ50 + Oly FL50 + TCON17 + Raynox 150 & 250