Here' s my opinion,

I own a NEF handi rifle in .223 Rem. Bull barrel, good scope. I love it. It will shoot 1/2" gropus at 100 yards. I doubt if a Remington or Savage wil do MUCH better. You are tied to one shot though, instead of a quick follow up with a bolt action.

I also own two different savage rifles, one is a .243 and the other a .308.
The .243 will shoot 1" groups. I do like it a lot for predator hunting, but I switch back and forth on whether to take the Savage or NEF.

As far as .223 or 22-250? The 250 is definitely flatter shooting, but there isn' t that much difference.

If both guns are shooting a 55 grain bullet, and both are sighted in 1/4" low at 25yards, the .223 will be 1/2" LOW at 250 yards, the 22-250 will be zeroed
at 250 yards. At 300 yards, the 223 will be 5" low and the 22-250 will be 3" low. That 1/2" difference isn' t much at 250 yds. ( this info is straight out of " The Gun Data Book" by F. Philip Rice )

No, I can' t argue that the 22-250 is flatter shooting, BUT that much difference isn' t worth it to me.
The .223 rem is cheaper to buy ammo, cheaper to reload, quieter, less recoil, (not that either one kicks much) and the 223 won' t burn the barrel out as quick.

This is just my opinion.