>>3597993I know the Canon lineup a lot better than the Nikon lineup, so take my Nikon recommendations with a grain of salt. Also, you said you want to go full frame and with your budget you're going to sacrifice some burst speed to do that. IMHO however high fps is overrated. So long as you have 5-6 fps and solid AF you're good.
You're going to lose reach going FF, but you're also fighting low light. If you're getting by now with an f/4-5.6 lens then I would think a D750 + AF-S 80-400mm f/4.5-5.6 ED VR II would cover you. You don't gain aperture but you do keep and extend your reach and the larger sensor will give you about 1 stop better high ISO performance. That combo used will run you $1,800 - $2,000.
The newer 80-400 is sharper but also a lot more expensive, and the older one isn't bad from what I've heard from friends. Certainly should be better than your current kit. What I can't tell you is how fast/well it focuses.
If you need light more than you need reach, then you're looking at getting a 70-200 f/2.8. I can tell you that the Tamron SP 70-200mm f/2.8 Di VC USD G2 lens is awesome and they go for $1,300 new. With a used D750 that's still within your budget.
On the Canon side I would recommend a used 5D mark III or even a new gray market 5Ds. The Canon 100-400 mark II is awesome and is probably the sharpest, highest performing 80/100-400 out there right now. And again if you need aperture more than reach, the Tamron 70-200 f/2.8 G2.
Why would I suggest looking at a 50mp 5Ds? You give up some speed (only 5 fps) and you have to be careful with the buffer when shooting 50mp RAW images (buffer is huge for JPEG). Doesn't seem like a sports camera? Except it has the pro AF that the 1DX bodies have and with that kind of resolution you can easily crop 2x, even 2.5x and still print 13x19 and 16x20. My 5Ds retired my faster but lower resolution bodies from sports/action/wildlife.
Hope this helps!