Both calibers are very good for yotes. Check out the ammo prices and availability - the .223 USED to be the more affordable and available, but our Iraq incursion seems to have affected both qualities of .223 ammo. I'm finding it more difficult to locate some of the .223 ammo that I like (like Black Hills).
With my eyesight, I don't shoot coyotes at the longer distances - over 150 - 200 yds., so the .223 is fine for me. If you'll be hunting in wide open areas (such as West Tenn.), then definitely the 22-250 is the way to go.
As a suggestion, don't scrimp on a scope, especially if you go with the 22-250 for the longer distances. Have fun!!!