For real world conditions, the 22-250 will burn very nearly twice the powder, for the same results. The 22-250 will shoot a little flatter, and would be a better choice if hunting type shooting, at unknown exact ranges, will be a large part of the menu.
Either will serve admirably for what you want to do. Pick the barrel you need.
If you are in a place where the number of gophers merits the effort, it will be easier to shoot the .223 all day.
The ability to spot your own shots is nice, too.
Cheers
Trev