I've shot both guns on rodent type varmints and the .22-250 has an edge in cutting through the wind.

Won't say it has and edge on distance as I've popped prairie dogs with my .223 at 550 yards.
Furtherest I've shot them with the .22-250 was 450. Reason is "it happened to be the gun I was carrying at the time".

One advantage to the .223 is the ammo is lots smaller and that's an advantage if you're walking the prairie hunting prairie dogs. I usually measured my ammo by the "quart" when I carried it.

Military cases aren't a cost advantage anymore for the .223 since bulk commercial cases are available. The commercial cases are easier to load than military cases as some of the old primer pockets (military) were a bit tight.

So, my recommendation would be to pick up which ever caliber you'd like. The .22-250 has an edge for velocity and wind bucking, but that's it.

I still have both rifles (in Model 700VS). Old Remingtons were the most accurate.

I do have a spare barrelled action in a .22-250 if you're looking for a project gun. Contact me if you have any interest.