Since you state 200 yards, I'd take the 22-250 over the 223 due to the 400+ fps velocity increase. I've now shot several deer with the old 60 gr Hornady hp loaded to 3500 fps. Every deer so far has been DRT. I have Wincherster 64 gr sp on deck for when the Hornady's are gone.
I just looked and did not see any Hornady 60grain HP in .224 listed.
