The .22-250 is not as good a deer caliber as the .223 Remington, provided the .223 has a 1:12 or preferably a 1:9 twist to handle heavier bullets.
My 1:12 twist Tikka .223 Rem will shoot 60 grain Nosler Partitions well (discovered today) and that's a good deer bullet. Most .22-250s around have a 1:14 twist which won't stabilize 60 grain bullets especially well. If someone made one that had a 1:9 twist, it would be a pretty good deer round for open areas if 70+ grain loads were available.
The next step up is a .243 and we've had three 10-12 year old grandchildren who've shot it very well.
“God save us from people who mean well.”
― Vikram Seth