i've shot coyotes with both .22lr and .17hmr, no comparison, i would put the .22lr at 50 yrd sort of thing and the .17hmr up to 150 yrds, you have the .22lr with slow bullets and slow twist barrels 1 in 16 from memory (not a lot of spin on the bullet) then .17 hmr going twice as fast with twice the twist (1 in 9 i believe) and you as close as your going to get to centerfire performance from a rimfire, killed over 20 for sure with the .17 hmr and my Dad has added a good half dozen or so to that and its a real 100 yrd killer, we generally never test it any further, but i've trailed some coyotes for way too long etc. with .22lr and just don't find them as easy to get inside 50 yrds as inside 125 yrds etc. so the .17 hmr is by my opinion about 8x more effective than a .22lr, sure you can get it done and some have done it with high power airguns too but i could hunt coyotes strictly with .17 hmr and get probably over 80% of them that i call in than if i had a centerfire in my hands, it wouldn't slow me down much if thats all i had to hunt them with
hope that helps
edit, that 80% is not meant as 80% success ratio on coyotes, pretty sure i'm not that good
....of the ones i do manage to kill every year with centerfire...i'm sure over 80% of them i could do with .17 hmr