This has less to do with the caliber then it has to do with the weight of bullet you are shooting.
I have been a bowhunter for the last 25 years, but when I moved to Colorado I found I had the opportunity to hunt archery early and rifle later in the same season. I didn't even own a rifle other than a .22.
My hunting partner had moved to Alaska before I moved here, so I knew if I was going to buy a rifle, I wanted one big enough to take to AK and hunt Griz. I read a book by M.L. Simmons where he extolled the virtues of the .338 Win. Mag. he stated that he shoots everything with it from Pronghorn to Elk. In his many years of killing animals he said that he doesn't get a coffee cup of ruined meat with that caliber, even on a small animal like a Pronghorn.
I went out and bought a Ruger M77 MkII stainless/laminate in the .338 WM and then went about developing a handload for it. I looked at the available bullet weights for it, and decided that because I was going to be using it for Deer and Pronghorn, that I wanted to use a lighter bullet than the 200-210-225-250 grain common weights. I found some Nosler AccuBonds in 180 grains which I thought would be perfect. I loaded them over IMR 4350 and found that with 73.5 grains I could keep 10 shots under the size of a quarter at 100 yards.
I shot a 5X5 Bull Elk last year ('06) on opening day at 30 YARDS, the gun went boom, and it ran like hell. No blood, no hair, no nothing. I tracked it down the hillside, and didn't cut blood for over 100 yards. When we gutted it out, the entrance hole was the size of a small fist, and there was NO exit hole. It had broke two ribs going in, and we found a hole in the stomach that we figured was where the bullet had turned and gone towards the back of the animal. I wasn't about to go digging through the guts to find the bullet. I was shocked about two things, first, that it actually ran after the shot (I figured it would have been doing backflips with a .338 WM at 30 yards), and two, that the bullet had not been a passthrough. It is entirely possible that the bullet at that close of range didn't have the time it needed to stabilize, and it might have been tumbling causing the large entrance wound, then didn't expand either, allowing the animal to run. It went close to 175 yards before it was down.
Hunting season '07 I shot a Pronghorn Doe in WY at 225 yards. The bullet hit her at the base of the neck, and my wife said it didn't even flinch, of course with a shot like that there was no loss of meat. A couple of weeks later I shot a Mulie Doe at 225 yards and the entrance was between the neck and the front shoulder with the exit through the heart and out the ribs also breaking the off side front leg in half. When I skinned her out, it was bloodshot from the shoulder to the back ham on the entrance side.
I think the amount of bloodshot on the Deer was caused from shooting the lighter bullet. I am going to take the off season and re-develope a cartridge in the 200 to 210 grain range. The theory I have heard is that the bullets in that range and higher punch through the animal so fast that it causes a vaccuum at the entrance and you don't get the bloodshot. This is only a theory I've heard, and I have no data to back this up but I figured I'd increase the bullet weight and see what happens next year.
If you're worried about the meat loss from bloodshot it might be worth it to investigate some different grain bullets and see if they cause less damage. It's sure cheaper than the other options of reconfiguring a rifle to another caliber, or buying a new rifle.
Good luck with whatever you decide.