I'm going to just add a quick note from experience as someone who has recently moved from DX to FX (D7100 to D810). I too mainly shoot wildlife, including small birds.
I held off for a long time due to the perceived view of DX number of dots is better than FX less dots, I almost bought a D7200 instead.
So far (and a lot of photos later), it's just not the case.
Lens for lens, I can crop heavily on the D810 and still have a far better IQ photo than I can get with the D7100. Ok, I know we are talking more MP rather than the D750 that is being discussed, but still, like for like and heavy crop still results in a far better photo than I can imagine with the D7100. In fact, the D7100 hasn't taken a shot since, but I do carry it as a backup.
MP debate aside, I can shoot at far higher ISO (and stay out later/get out earlier) than I would ever consider with the D7100 and living in the UK even on a nice day, I tend to be shooting at ISOs in 4 figures and the AF for wildlife is far better (although the D7200 is supposed to be close).
Just my experience over the last few months. When I get a chance, I will be doing a like for like comparison and adding it as a blog on my website.