Having both and using both, My .22lr's will work out to 50 yards easy, but they mushroom out too much if not a higher speed round on impact or at a longer range on impact. The el cheapo plinking rounds will not do unless its close in with a .22lr, they just don't penetrate the skin very well for me.
My 17HMR 20gr FMJ's are best, followed by the hollow points (although they stick/jam on the barrel during loading sometimes, so I'm not going to use them anymore unless I figure out how to remedy that) and lastly the polymer "tipped" rounds that splatter on impact, and for me the polymer rounds seem somewhat useless on anything bigger than a Squirrel/prairie dog sized critter or target shooting.
The FMJ do the job for me out to 150 yards. I was doing penetration tests and was blowing through wet wood 6 inches thick @100 yards with the round staying in tact. I haven't put them out further yet to see what the limit was. I was really impressed with the power of them compared to the 22lr. The Hollow points stayed together up to 75yrds always, and sometimes up to 100yrds.
If you want to make sure your critter doesn't run more than 10 yards, you'll need a lot of lead flying through the air as in 12g slug, a mag center fire round, or you need to be a good shot, and take head shots, spine or heart shots (and honestly there aren't a lot of angles to hit the heart directly without clipping something so I don't aim there unless I'm ready to walk it down) I have taken yotes with the hmr without issue, but now that I have a .243 that opens up lung shots, so if that is what I go out for i'll be using the .243 As far as Fox' go I think the 17hmr will down them all day, especially inside 50 yards.
So to explain my reasoning this is how I hunt. I'm not a run and gun kinda guy. I don't squeeze the trigger unless I'm fairly sure I'm going to hit exactly where I think I'm going to hit as I dislike the "finish off" shots. (I pass as much as shoot) All rounds have physical limitations, the X factor is the shooters limitations to get the most out the round in question.
Inside 50 yrds as you asked, either will work fine with a good hit. If not a good hit they will no doubt run more than 10yrds with either round as neither present devistating power that will bring them down without a precise hit.
That's my 2 Cents.. and worth just about 2 cents in today's market!!