I can't speak for anyone else but I switched from Nikon D850 because I tried the a9/200-600 combination and found:
1. The autofocus was much much better for birds in flight - and for me specifically smaller fast erratic birds.
2. The 200-600 was on a par with the 500PF in terms of sharpness but less than half the price and the combo worked exceptionally well with the 1.4TC at 840mm - even for birds in flight. A dream for wildlife and birds really.
After quite extensive use there are a three main things I find that are important:
1. autofocus points covering 80+% of the frame - makes tracking easier since smaller subjects can be anywhere in the frame without losing focus
2. short throw(1/4 turn) zoom to assist with quick focus acquisition - zoom out to acquire focus and then zoom in with one finger.
3. evf with little or no blackout or lag to make keeping the subject correctly positioned in the frame as long possible.
And then there are other benefits such as:
20 or 30fps means many more chances of getting good wing position/composition
Having 40+MP (a1/R5) means being able to crop to improve composition without any major loss of details
Shooting at high iso (6400 - 12800) and get excellent image quality means shooting at higher shutter speeds and higher percentage of tack sharp images - you can pretty much eliminate motion blur at 1/8000s. You get lucky occasionally at 1/3200s but more misses than hits with small birds.
Not having to worry about rolling shutter distortion with small fast birds means no weird misshaped wings or heads/bodies.
Both the a9 and a1 can autofocus at f9 so shooting birds in flight is no problem at 840mm (with the 1.4TC).
Both the 200-600G and 100-400GM have minimum focus distances of less than 2.4 meters so you can fill the frame with small birds - not possible to the same extent with a 600mm prime lens with MFD of 4.5 meters.
A secondhand a9 is pretty inexpensive now so coupled with the 200-600 and TC1.4 you get a top class wildlife system that to this day is still very hard to match.
I have used the R5 100-500 combination and that is very nearly as good as the Sony systems so if you're a Canon user you would probably just stay with Canon. However there are a few situations where the R5 does not keep up with the Sony cameras, including:
30 fps vs 20fps
In some situations their autofocus struggles to do a very good job. I found their subject recognition and acquisition was faster than the a1 in most bird situations but for actual af tracking the R5 has more misses for some reason. Still above 90% in my use but quite a lot more misses than the a1.
There is more of a difference with small birds in flight where rolling shutter distortion is going to become hard to ignore unless you switch to mechanical shutter. And the additional evf lag may become an issue in some situations.
Neither of the latter issues bothered me but I didn't test the R5 in every situation.
The 100-500 is nice but the zoom throw is rather long so a bit awkward to zoom while shooting. Also not quite a match for the Sony with the TC1.4 it seems. The extra bit of reach is not huge but it does mean 15% more pixels on the subject.
I am just a hobbyist but have been able to capture images that I wouldn't have though possible. Some examples of swallows in flight - and you should view these fullscreen on a 4K or 5K display for the best viewing.
a9 200-600 1.4TC @840mm
https://duncangroenewald.com/img/wildli ... 57_DxO.jpg
a1 100-400 @400mm
https://duncangroenewald.com/img/wildli ... _DxO-1.jpg
Despite what it may look like the background was not clear sky, it was rippled water and bush, the worst background to acquire focus against - the subject is that close so bokeh is such that you would be forgive for thinking the rippled water is the sky.
If the R3 was 45MP it might interest me but at 24MP it is really only matching the a9 - and presumably it will be a lot more expensive. So all I would be getting is 30fps.
The Z9 if it is 45MP would be interesting but Nikon has no 200-600 available yet and it will probably more expensive than the Sony 200-600.
After trying the Z6 I decided I wasn't going to wait. In retrospect that was a good decision because otherwise I would still be waiting.
I think you will find many that have made the switch have similar reasons, however I would be equally happy to be using Nikon or Canon if they could provide a similar system at a similar price.
Ergonomics and colours have also never been the reasons I have missed shots.