I would say all the "tests" have been done.
22 Mag- trappers gun
17 Hmr- bench gun
22 lr- off hand fun gun
I like them all but, probably the 22lr the best.
I did not shoot any coyotes with the 17hmr, because it had enough problems anchoring Woodchucks. In my experiance the either of the mags make fine off hand 3 position varmint & fox calibers. When you add bi-pods and big scopes and start shooting them past 100 yards, the result is woumded critters, slow death. At that range the accuracy differance between the 17hmr and mag don't matter. The mag is certainly "varmint moa" at that range.
For woodchuck size varmints your gaining about double the range of a 22lr for kill power. Sounds like a lot......."double" but it's only 50-60 yards. I like a 22lr for walking varmint off hand / 3 position. Most all of them will shoot 1" and under at 50 yards (varmint moa) and kill about the same as the mags do at 100 yards. And there fun.
If I ever buy another mag/hmr it would likely be set up just for off hand varmints in a sporter weight, 4 x fixed or 3-9 scope,shooting sling,etc; which tends to keep you with in it's kill range. Mag,hmr or lr I have come to favor the semi auto for off hand varmints. Little loss in accuracy but, still easy "varmint moa" at that range, more fun, follow up shots,etc. Or maybe a 17hmr just for bench.
If money was no issue a well balanced Volguartsen semi auto in sporter weight, 17hmr, with a quality 3-9 varible compact scope would be ideal for off hand varmints.
That would be the ideal off hand/ 3 position rim fire varmint/fox rifle IMO............that would be special /ubbthreads/images/graemlins/grinning-smiley-003.gif