Either will give you a non-survivable wound, no matter the medical help available.
Good thing you compared the 223 and 338, because about 10 years ago I worked with a guy that was shot at about 300 yards with a 7mm mag. It hit him in the left butt cheek and blew out his hip/pelvis bones. Butt Shot Bruce was in the hospital for about 3 months if I remember right. He even turned down dissability and came back to work at the sawmill.
Sorry, I know this was off topic but most of this thread is anyways. Don't really know if he would have been better or worse with a 7mm-08.
