The 243 with a 95 Berger is plenty bullet for any deer in America out to 350 yds (even further) providing you're only taking mostly or fully broadside shots. I wouldnt try a "Texas Heart Shot" or sharply quartering away at 350 with one however.
Your answer really depends on how you hunt and what you want to use. Which gun are you most confident with? Which one do you have the most trigger time with? Which one do you have the most ammo for? Which one do you enjoy shooting the most?
If there's LR running shot possibilities, or if you don't usually have or take the time to wait for standing broadside shots, or if you're likely to only get a brief glimpse of the deer before the shot and can't afford to be picky about body position of the deer, I'd say use the 308. If you sit and wait overlooking openings or fields or can realistically expect broadside shots, then the 243 is plenty and then some.
Good Luck on the hunt.