ballistically, both are very similar. Contrary to common belief, the 22-250 is neither latter, nor more wind resistant - compare a 40 grain .204 at 3900 fps against a 60 grain .224 at 3600 fps - the 204 bullet has a higher BC, so - faster, flatter, less drift. A non-standard twist in the 22-250 will stabilize a heavier bullet, which will perform better at extended ranges, but inside 500 yards or so, the 204 is still ahead.
The 22-250 will deliver more energy on impact to larger targets (like coyotes), but this comes at a cost of recoil, which means you won't be spotting your own shots through the scope. And for targets like gophers, this is half the fun. That, and the 204 burns less powder, which means it heats up barrels slower, so you'll get more shots downrange between cooldowns.
so - for coyote-sized varmints, the 22-250 is probably ahead. For gophers, the 204 wins hands down. For target shooting at the range - I'd go with a custom barrel 22-250, shooting 75 grain VLD's