Wow, this is turning into a very interesting thread (for me anyway ;-). First of all: thanks for chiming in everyone. Some responses:
@Hotdog 321:
Wow--you are shooting in a seriously crummy gym! My sympathies. I can generally get away with f/2.8, 1/500 sec. at ISO 3200 or even 1600.
Yes, crummy is right. No natural light at all, dark walls, and fluorescent tube lights that are, for some idiotic reason, fitted in plastic cases that lower the available light and, I imagine, were white at some point in the 1970s. What also doesn't help is that 1/500 tends to be too slow if I want to stop the swords as well as the combatants (I'm shooting sword fighting ;-). Also, the combatants are dressed in all black. I have an OK exposure at ISO3200 (i.e. correctly exposed background) but then the combatants are basically silhouettes - I want to be able to see the fabric of their protective gear, the way their arms mode, and maybe even a hint of a facial expression through the mesh of their fencing masks. All without flash, of course (I can get away with it during training, but not matches).
@TTMartin:
If you had a full frame dSLR. It would have gathered one more stop of total light from the f/1.8 and 1/640 exposure. While the cameras ISO setting would still have been ISO 6400, the amount of amplification required by the full frame camera would have been less. So the photos taken with a full frame camera would have the same amount of noise (or less) as your 50D at ISO 3200.
That one extra stop is 'simply' the result of the physically larger sensor, no? I guess I was hoping for even less noise (>1 stop) due to a newer generation of sensor, as well (2014 Nikon D750 vs. 2008 Canon 50D). Is that unrealistic?
An f/4 lens takes away all of the advantage and then some of going to a full frame camera. You'll actually be over one stop worse than your 50D with a f/1.8 lens.
Yes. Like many seeking to upgrade to FF for the first time, I guess I was expecting miracles.
At f/2.8 you will be at ISO 16,000 to equal an f/1.8 lens at ISO 6400
Also correct: I 'forgot' about the third stop between f/1.8 and f/2.0 in my 'calculation'.
You might consider the 7D Mk II with its light flicker synchronization.
Does the Canon EOS 7D Mark II's Anti-Flicker Mode Really Work?
And keep using your f/1.8 lens.
I have seriously considered the 7D mkII. The auto flicker mode seems useful: I do experience uneven exposures within bursts. If I were exclusively shooting (outdoor) sports, I guess it'd be a no-brainer (especially on a budget). I'd even be able to keep my current lenses. But to me, there's two things that make the mkII less desirable:
(1) I'm not entirely convinced that it would be a sufficient improvement in high ISO compared to my current setup: in this gym, I'd still be shooting at ISO6400 and frankly, looking at the studio scene, that doesn't look too impressive (maybe 1 stop better than my 50D).
(2) As an amateur, I plan on having one body which should serve other purposes as well (actually, primarily other purposes). None of those other purposes are outdoor sports or wildlife/birds, so the value of the 7D mk II (over e.g. a D750) seems to be mostly a better AF system (useful for 1 of my activities) for which I sacrifice resolution, dynamic range etc.
My 1.8 primes are actually insufficient for this very specific purpose also (although I absolutely LOVE them in general): the 50mm f/1.8 seems to be the perfect focal distance, but focuses too slowly for fast action. The 85mm f/1.8 is certainly fast enough, but it's too tele: there's only so much space in a gym before a wall blocks your 'feet zooming'

.