I've been shooting with Sony E-mount gear since 2011 - I started alongside my DSLR, just bringing it as a second body as the early E-mount cameras were too slow for moving birds and didn't have much lens selection. As the bodies got better and faster and more lenses came along, I started using the E-mount almost equally with my DSLRs - splitting time about 50/50. Once they got to the A6000 series cameras, which were the first ones capable of bird-in-flight shooting, low light situations with ISOs of 6400 without NR needed, etc...I really started using the E-mount cameras more for my wildlife and birding, especially once I was able to add a decent 70-200mm F4, then a 70-300mm, and finally the 100-400mm GM lens plus 1.4x and 2x TCs, which is really an excellent lens and still respectably light.
Last year, after shooting my A6300 with 100-400mm lens against my DSLR and a Tamron 150-600mm, I just decided to go ahead and sell off the DSLR kit, and just stick to the E-mount going forward. The A6300 is able to shoot every type of bird and wildlife photography I need it for - it has good reach, is handholdable all day, the body is very small and light yet retains good customization of buttons and menus so I can put all controls where I want them, it has memory banks so I can store sets of 'still' and 'BIF' settings for quick switching between the two, and the autofocus is fast and reliable in all lighting conditions for single focus plus has very good continuous autofocus depth tracking for flying birds of pretty much any speed. Importantly too, starting with the A6300, the electronic viewfinder went to real-time refresh at 8fps, so no longer having that harsh blackout period and no slideshow effect when tracking a moving bird and panning. It still has a 'blackout' similar to a mirrored camera when the shutter is flapping up and down, but it's not showing you a slideshow of the last image taken...in between the shutter shots, you're getting a live-view. It's not quite as advanced as the A9, which has zero blackout, but it's the next best thing and makes EVFs finally equal for panning/burst shooting for me.
Currently I'm still shooting the A6300 and FE100-400mm GM combo, and also have the 1.4x TC for when I need it. The A6400 is likely going to be nearly identical in performance in virtually all modes, with one exception - it has improved the 'real time tracking AF' mode which supposedly locks on and tracks more reliably than the A6300/6500's 'Lock on AF' mode...and the A6400 is going to get a future firmware update that adds 'Animal Eye AF' tracking, which the older bodies won't get. I don't use the lock-on AF tracking mode on my A6300 - instead relying on AF-C with wide focus area - the camera can stick to the subject and track it through the frame as well as keep focus on depth tracking, so I've never really felt the need for a subject-tracking lock mode. If it worked more reliably, I might try it out on the A6400.
I've got a huge gallery running of shots taken with the A6300 for birding and wildlife - I tend to post almost everything for the first few months as I'm sharing on some birding forums where some shots are intended as ID shots and not necessarily as 'beauty' shots...after a season has passed, I'll get rid of some of the ID shots and keep what I consider the nicer shots...so excuse that the first 5-6 pages of the gallery have lots of shots including everything then as the gallery goes on, it tends to be more the nicer shots that I'm keeping up a bit longer:
https://pbase.com/zackiedawg/a6300_wetlands
A vast majority of shots will be with the FE100-400mm GM lens, for the past 2 years or so...before that, most of the shots will be with the FE70-300mm G lens or Tamron 150-600mm lens.
