I've used the 17rem and 204 for coyotes, for 5+ years. My 204 is now AI, but the commercial cartridge itself is just fine for coyotes. I'm not posting any of this to sound arrogant, just giving you a bit of my background...
I average about 100-120ish coyotes alone, a season. I don't know how many I've killed with my 204 or 17, but I've never lost one. I can remember multiple 400-450yd shots with my 204 and DRT. Ackley improving it made it that much sweeter. My 17rem I have sold last year, but it was nothing against the rifle or cartridge, I just got offered a great deal. I would never, and will never, have any problem taking either to a stand with me and be very confident doing so. I'm with you 100%, I'll always have a 17 center fire in my safe. But I'd be lying through my teeth if I said the 204 didnt have advantages over the two
The advantage IMO, is as mentioned above, the 204.. Factory loads in a 204, are somewhere around 4200fps. You'll have a heavier bullet than the 17, shooting just as flat and just as fast, but hitting harder down range. It's a win win situation. But I'm by no means dogging on the speedy 17. I'm only trying to give you my experience with both.
Both do great on fur, if that's your intention. They both handle coyotes just fine with factory ammo, and excel with handloads, again, if that's your intention. So if I had to choose one or the other, I'd have to choose the 204. The 20cal will just have more spunk down range. I'll admit that's nice to have too, we're all human, and can't always thread the needle.. Good to have some backup. I hope any of this helps.