Whatever you do, in a .338 don't use a light bullet!!! Factory Hornady 180's are rated at over 3200 fps, and has already been said, velocity tends to cause far more meat damage than the size of the bullet, unless you are talking a really small diameter bullet.
It's not the size of the hole as much as it is the shock wave going through the surrounding tissues that causes meat loss. I have been deer hunting for 30+ years and have shot 27 deer in the past 10 years alone with a .450 Marlin and a .444 Marlin. While I do my best for a head/neck shot or a broadside through the ribs, with 350 gr RNFP .45 bullets, I can screw up and punch a hole through a shoulder and almost eat right up to the hole. With Hornady 325 gr. LeverRevolution FTX bullets at the faster speed, hit a shoulder and it is a loss of the whole shoulder. That extra 350 fps out of the muzzle really shocks the muscle mass. The best part about the big slow bullet is that the animal stops and falls over, rarely any chasing of wounded animals.
Most of my hunting partners use their moose rifles for deer - 308's, 30.06's, wm's etc... and they have far more meat loss than I do, and they never have bang-flops unless it's a head/neck shot.
On the other hand, my cousin hunts areas where 300+ yard shots are the norm, and he uses a 7 mm RUM with 140 gr bullets at over 3600 fps. With the tiny bullets he swears that he gets less meat damage during rifle season than he gets with his 45 cal during muzzleloader season. And he's been taking 3-5 deer a year for over 40 years.
Take a slow moving RNFP 170 gr. 30.30 vs a faster 165 gr. .308 and with the same diameter bullet, and the exact same shot, you will typically find that the 30.30 will put the animal down faster, and with less meat waste.
By all means use your .338, but use larger heavier bullets at a slower speed and just be sure of your shot and have fun!