There are far more bullets in .30 caliber, especially target-grade bullet, and even in hunting bullets the 8mm selection is a little thin. Barnes, for instance, only makes the Tipped TSX in a 160-grain, though they also have a 200-grain hollow-point TSX. But the 8mm selection is adequate for just about any kind of big game hunting, whether local whitetails or big stuff. There's probably an edge to the 8x57 on larger game due to several premium bullets in the 200-grain class, including the TSX, Nosler Partition and Norma Oryx.
There a lot of relatively low-cost .308 brass available, including military. 8x57 brass is relatively scarce, but rarely unobtainable.
The .308 may be more inherently accurate (if such a thing exists), but the 8x57 is certainly very accurate.
