The .22 mag will kill smaller varmint sized animals much more decisively than the .22 lr. I've shot big Texas jackrabbits with .22 lr's in nearly every kind of situation you can imagine, and believe it is marginal for them. I've seen many big jacks take multiple hits and keep on moving, sometimes up to 100yds.
I have also shot them with a moderate load in the .22 Hornet, which should be slightly better than the hottest .22 magnum loads. The Hornet just slaps em down, leaving a half-dollar sized hole out the back side.
I wouldn't hesitate to use the mag on a coyote, out to 50, maybe 75 yards. To say the .22 lr will do anything the mag will do is just wrong, in my opinion, of course.