For equal weight bullets, there won't be a lot of difference in BC. In theory, the smaller the bore, the better the BC for a given bullet weight, but it's also a matter of sectional density, and they end up pretty similar.
If you buy a .22-250, you'll see coyotes outside your range on a windy day where you wish you had a 75grn+ pill to reach out and tag them. If you buy a .243win, you'll roll coyotes at 30yrds and kick yourself for how much damage it caused.
Not that the .22-250 is particularly kind to hides either, but moreso than the .243 of course.
I don't have a .22-250 anymore, as I favor .223rems. But I also have a .243win, and I'm drooling to get a .243WSSM from Dtech.
As a side note, the longer I hunt whitetail deer, the more and more I start to consider the .243win the optimum whitetail cartridge (even though I rarely use it for that).