I would assume then the fireball would be better on fox and if i'm lucky the occasional yote. Are there any affordable fireballs out there, my options are limited by cash so i was actually thinkin of the 22mag.
17 HMR is rimfire. Cost is $12-16 per 50 shots.
17FB is centerfire. Only 2 kinds of factory ammo available and you're looking at $25 or so for 20 shells, which can be hard to find, BUT it's reloadable. The 17FB is basically the commercialized 17 Mach IV wildcat, which has been around for decades.
I would NOT use a 17HMR on a coyote unless it was within 50 yards and I had a steady rest on a still, broadside target. I would stretch the 17FB to 200 on a broadside coyote, though I still believe with most ammo, the 17FB is marginal for coyotes. Now step that up with hand loaded ammo with premium bullets and you've got a consistent fur cartridge.
The 17FB has a LOT more power than the 17HMR. Max range on fox would be about 100 yards for a 17HMR. A 17FB will easily stretch to 300 yards.
Remington is the only one that ever made them in bolt guns. There's still a few new ones out there, but supply is drying up. You can still get TC barrels (and aftermarket TC barrels like MGM and Bullberry) in the 17FB.