The only difference between say a Remington 700 and an AR-15 is barrel length and twist. My remington run a 1:12" twist for bullets up to 62gr. Mine prefers Hornady 50 gr V-max. AR-15 or an SUR as I like to call them will have a 1:9" twist allowing you to shoot bullets up to 70gr. For bullets in the 70 to 75gr weight class a 1:8" twist. and a 1:7" twitst for anything over 75gr.
So other that twist nothing really your velocity may be a little lower with an ar because it is gas powered.
Since the semi-auto .223 is usually gas-operated delayed blowback, it makes no difference to either rifle on a pure Ballistics level...
BUT, most people go through a Mental Process when using a Bolt-Action because they know the First shot darn well better be on target...because of the time it takes to load a second round & get target re-acquisition.
On the other hand, those who were initially trained on Bolt-actions tend to keep that same habit when using a semi-auto and tend to shoot MUCH more accurately than people who have never spent serious time with a bolt-action rifle.
So, really, it's a choice that can only be based on what you personally prefer to do.
+1 on what B.Shrek said. Any differences in ballistics & accuracy would be so small you wouldn't notice,just make sure you can get the correct twist rate in a bolt action. Alot of mfg's put a 1-10/1-12 twist in bolt action barrels and that will really limit your ammo choices. I prefer a 1-8 twist in 223 cal,that way I can shoot anything up to 77gr and not have accuracy problems with tumbling. I usually shoot 55,62,68,and 75 gr bullets and I handload my ammo.