The 22-250 has a little better ballistics, shoots flatter and hits harder. The advantages of the .223 is that ammo (especially brass for reloads) is cheaper, its a little more friendly to your ears, and recoil is so mild you can often see bullet impact through your scope. Those advantages probably matter more for things like prairie dog hunting than yote hunting though. They are both pretty accurate rounds and both will shut down a yote pretty quick so its pretty much personal opinion.
In my experience whether your calling, spot and stalk, or tracking, shots over 250 yards are fairly rare. When calling the yotes usually either run me over or dont show up at all. Actually, I've killed alot more dogs with 12ga #4 buck than anything else and we dont even carry rifles anymore when we hunt as a group.