I had a stable full of .22-250's. It's a great cartridge but I now have five .204's (three AR's and two bolt rifles). The last .22-250 got turned into a fast-twist .243 AI this year. Reasons? It began with the desire to call my own shots. You can't always
see 'em but a lot of the time you can. Second, fur friendly. (Nonissue for pd's only.) Third, less barrel heat. And, fourth, less expensive to reload.
You'll need a fast twist .22-250 to get appreciably more range than a .204 but a fast twist .204 will still keep up. (Run the numbers.) You'll need a muzzle break on your .22-250 to call your own shots and it makes it painful for your shooting partners to shoot around you. Ask me how I know.
My AR's are actually more accurate overall than my bolt rifles. All of them (bolts and AR's)will shoot around 1/2 MOA or less with their favorite loads. For me, when I get past the capabilities of my .204's, I need my .243AI to gain enough range and energy to make a difference.
The AR platform is a different beast but it sure can clean off a pd mound in a hurry! It can irritate your hunting partners though...
I 'm just relating my experience. I hope the .22-250 shooters aren't offended. The .22-250 is still the King of varmint cartridges and the energy of the .22-250 does
make a difference on coyotes past 300 yards. But, after some pretty extensive use of both, I like the .204. Its a pretty amazing little cartridge.