For me it depends on the target and distance. Stuff to about PD size to 200-225 ish max, I may try an AR next time I get a new varmint shooting toy. My buddy used one on PD's to about 200 and had a ball, most were 75-150 yard shots. Would be good to have when multiple coyotes come in too.
Smaller targets like sage rats, I want a bolt action for the best accuracy possible, and the same if I am stretching things much past 200 or so. So far all my varmint guns are bolts, except for .22 LR. My favorite is a CZ527 in 221 Rem Fireball. That single set trigger has become my fav on a varmint rifle. Once set, it breaks somewhere between a whisper and a breath, or about 15 oz., I love that thing.
May get another CZ527 for the single set trigger, but a Howa mini-action has been calling my name too. Both are high quality mini actions, which I like for varmint rounds.