I've had the two different versions of the 500 f/4 for about 12 years. I was lucky and the first one was sharp. The second one (Series II) is not really much sharper, just lighter and more consistent with the TCs.
I have borrowed the 400 f/2.8 II, 800 and the 200-400 from Canon CPS and rented the earlier EF 600 in Africa.
The 800 was limited by its long MFD and the fact that atmospherics became a problem when I tended to try too hard to reach out. The 200-400 offered no advantage to me as I already had the 100-400 and 500. The 400 f/2.8 II was sadly defective and never gave a good shot while I had it. I did form the opinion that it gave me no functional advantage over the 500.
I am far from an expert and way too weak to handhold any of those for more than a few seconds.
I have settled on the 100-400 II and the 500 II and will probably stick with them until I am too old to go out shooting. I use the Series III TCs and both work with my 500 quite well.
I just sold my 5D MK III and picked up a refurbished 5D MK IV. I am impressed.
We are planning on going to Costa Rica in February for birds. The lighting is usually less than optimal in the forest gloom.
Subject to revision, I'm hoping the 100-400 (±1.4X TC) will be riding on the 5D MK IV and the 500 (±1.4X or 2X TC) can be used with the 7D MK II. I shall be forced to mount the long lens setup on either a monopod or a tripod. That may be too slow in the forest so I am still considering.
I loved the 600 in Africa but it was ALWAYS mounted on a gimbaled vehicle mount. If that were something I could count on, I would go up to the 600 in a heartbeat. Even the new model is really big.
I may be rambling here. Please forgive me if you feel so. The 500 is so handy and usable that I take it places I would probably not take a 600.