What do you want to do with the 22-250? Barrel burner 40 gr HP at lightning speed or 75-90 gr SMK for long range? I got a 250 last yr with a 26" 1:14 bull barrel. It's fun at the bench, but absolutely beyond worthless as a pickup gun due to the length and size.
Heavy barrels are nice if you're gonna go shoot a bunch. Wear inside increases rapidly as the barrel heats. Bull barrels will allow more shots back to back before cool down, but take much longer to cool. If you're going to shoot sage rats, it's best to take as many irons as you can. Then you can switch between them and keep from burning a single one down.
Personally, I'd go with the lighter barrel and try to maintain self control with round count. Slimmer barrels are so much more handy offhand or rested on the pickup mirror.
Either way, you can't not smile watching things turn to vapor downrange of a 22-250.
Oh and 220 Swift might even put a bigger smile on your face...
Greyson