They are pretty much ballistic twins, so if you were starting out and didn't have either, for me, it would be an easy choice and I'd go with the 22CM all day long. Mostly, because you can buy good 22CM brass that is ready to go with no fireforming and why not skip that step if you can.
But, if I already had a 22-250AI that I reloaded for, unless I just wanted something different, I'd likely rebarrel it right back to another 22-250AI.
Also, I think the larger hot rod 22 cals like the 22-243 Improved, 22-6mm, and 22-284 are better suited for shooting the bullets in the 75gr and heavier range, than is either the 22-250AI or 22CM
For a good all around varmint/yote gun, I think it's hard to beat a straight 22-250 shooting mid weight bullets.