frankly-unless you are shooting very long distances,I consider EITHER the 338 federal OR the 8x57 WAY OVERKILL for deer.Black bear,yes,but deer?I've dropped over 30 with my 6.5x55 swede-INCLUDING a couple of black bears,all one shot kills and nothing went farther than 20 yards max.Even at distance-the little swede can reach out farther than most guys can shoot.As far as deer ''running''after being shot-I suggest most,if not all of that would be attributed to bullet placement-not using an 8x57....
6.5X55, 7X57, 8X57, 30-06, 303, 8X50R (take your pick of Siamese, French or Austria all are the same length slightly different cases and bullets), 7.65X53, 30-40K, 7.62X54R, 6.5X50R 7.7 Jap, are all answers to the same question. What should our late 18th, early 19th century army use as a military cartridge.
If you look at all of them thyr range from .264 to .323 with just a few steps of .284, 308, 311, 318, and 323.
All throw similar weight bullets from 140 to 175 grain about the same speeds of 2500 to 3,000 FPS. All generating about the same foot pounds of energy give or take a few hundred.
All were pressed into hunting rounds as empires expanded or surplus rifles were made available post wars.
Saying one is greater than the other or over kill for deer is folly. All generate about the same foot pounds give or take.
With some actions being stronger than others it has allowed experiments with some of the loads and cases.
The Mauser 98, Arasaka, and Springfield actions being the strongest and able to handle sportsmen making the actions and cases do more than it was designed for. The 94, 93, 95 and 96 mausers being the next weakest and the open top actions like the Enfield, Manlicher, Mosin, Kraig being the weakest.
Arguing the 338 over the 8X57 mauser in a sporting load is like arguing 280 Remington Vs 30-06. Same basic case similar bullet designs and weights moving at similar speeds.
Don't get me wrong I like 6.5X55. I also like 308 Win and can not tell the difference between them down range. Bang, flop- sometime a stumble and a return to their feet for a short run to go find a better spot to take the nap.
There may be some bullet and cartridge combinations that are marginal for deer but there is nothing over kill. Meat damage is another topic but again similar bullets weights and diameters at similar speeds are going to cause the same kind of holes.