Opinions will vary as we each find our own niche that fits our circumstances the best. But with any cartridge shot placement applies... a splash is a splash and a punch through is a punch through no matter which cartridge you're shooting. Both usually means pelt damage.
The 17's are well known as being great fur savers. I've had and used most of the different 17's over the years, and consider them the best choices for most predator hunting for fur. They hit hard and stay inside more often than not, so all you're sewing up is the small entrance hole. They pretty much retired all of my 22's for predator hunting years ago. The 22 Hornet is also easy on pelts, as are some of the smaller/mid sized 22's, and they too will often not exit.
For thin skinned fox a 17 Ackley Hornet or 22 Hornet/KHornet is a perfect match IMO. But even they will exit sometimes on fox. The other smaller case 17 wildcats and 22's will work too, just not as fur friendly. The under rated 17HMR works quite well on fox too and is very easy on pelts.
These cartrides will all work well on bobcats too at their reasonable ranges for them, but the mid sized 17's and 22's are a better match at 200 yards and beyond.
Anything more than these is too much gun on the smaller predators if you want perfect pelts from them every time. Sure, some of the larger carts will stay inside sometimes as well, but when they splash or punch through they can really tear pelts up.
For both species and your 200 yard limit, in order of preference I'd opt for...
17 Ackley Hornet or 17 Ackley Bee (or if coyotes were possible too a 17 MachIV/17 Rem Fireball)
22 Hornet, 218 Bee or 221 Fireball for coyotes
They'll all work on coyote as well at appropriate ranges. But my favorites for coyote was the 17MachIV and 17 Remington, simply because the shots were often much longer than 200 yards here in the west. On the larger predators they too will usually not exit. They shoot flat and give extreme hydrostatic shock to make up for the smaller bullets. When the winds blow hard and the range is longer the 17's are pretty much excess baggage though when it comes to perfect shot placement. That's when a 22-250 or one of the 24, 25 or 26 calibers gets the nod.
FWIW-YMMV
