I love the 22-250 but I'm about to sit down for hours to load another 1000 rounds of ammo for it. Yes you can buy it but it's more expensive and less accurate. So that's my draw back on it.
The .223 guys can buy theirs buy the 1000's for the prices where who cares if it's not match grade ammo. And it will work perfect for coyotes.
I like the one gun for all around concept. I'd pick the 270 win. Doesn't tear up a coyote any worse than any other gun most times. Coyote, and anything else in north america.