I don't shoot birds, but most of what I shoot moves.
Our 1dx has great focus, good file, really good file which belies it's size and shoots about a billion frames a second.
Actually you can shoot cut frame video with it, by shooting stills.
Tethers (which probably won't concern you) like nothing in this world with ethernet.
We shot 8 to 9 thousand frames without ever crashing or restarting the computers.
I've never had that happen before.
Downside, not file size for me as it has great detail, good iso, though like all cameras once above 800 to 1000 you will see some behind the curtian smoothing.
Doesn't process well in lightroom (yes we've calibrated a lot) processes real well in c-1 (1 stop brighter in c-1 vs. lightroom, processes even better in DPP and raw developer, though DPP is bog slow.
Compared to today's dslrs it's expensive and probably will stay that way as it's huge well built and 100% professional.