My only .22 magnum wasn't all that accurate, so I've little experience beyond tin cans at 40-ish yards.
I'd call the Mach II devastating on prairie dogs to 100 yards, and adequate to 200. I therefore assume the .17 HMR would work to probably 250. Wind is more of a problem than distance.
Coyotes? I wouldn't use either cartridge, absent head shots at relatively close ranges, as inside 100 yards.
My prairie dog hunting was a drive-and-stop process across a private pasture, just shooting from the cab of my truck. There were lots of dogs that would pose for us at distances well inside 300 and 200 yards. Numerous shots around 100 yards. If I lived nearby and regularly went out for them, I'd probably go with the .17 HMR.
That said, I've had fun on PDs with a .223, a .220 Swift and my .243 with 55-grain bullets. My choice as a sometime visitor, I guess, would depend on the mood of the moment.
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