The .22 mag would definitely be better on coyotes and perhaps fox as well - within it's accuracy range. Some newer guns do shoot well, but even a cheap little Marlin .17HMR will usually group into 1/2" or slightly less at 100 meters.
The polished GM barrel on my Martini gives be concrete 3/8" to .4" groups at 100 meters and is pretty much a gaurantee for head and chest shots on our ground squirrels at 200 yards. We draw the line at 240 yards as being about max. Longer shots are quite possible, but we can't be sure of a chest hit, which is necessary at that range to 'stop' them.

The HMR is a wonderful round.