I own both and I have used both for about 40 years, although I have used the 308 more. That is not to say I like the 308 more, but I can't say I like it a lot less either. I usually go for a 30-06 or a 300 H&H in a bolt action but in autos I have shot more cases of 308 then I can count in my life.
The 8X57 has a lot less different bullets available to the US shooter unless he shoots imported bullets. (As has been notes already several times)
But if you are not adverse to using the imported European bullets there are probably far more 8MM .323" bullets available then you'd really ever need and they cover everything from varmints to deer sized game, to elk size, to target shooting and long range paper punching is NOT a problem with the 8X57, (if any shooter wants to use it for that)
I see the posts about the long heavy .308 bullets, but the truth is that the slight advantage of the 30 cals BCs shot from a 308 Winchester is probably equaled by the slightly faster velocity available from the 8X57 firing bullets of similar weights. If both cartridges were chambered in barrels and are installed in the same action, the bolt thrust at a given pressure and the strength of the action holding them both is the same, so with more volume of powder burning at the same pressure the 8X57 is usually out run the 308. But not by very much. From the standpoint of reality on targets or game I would say the difference is actually meaningless.
As of right now, the only bolt action 308 I own is a Mossberg MVP which is rather utilitarian, but it's very accurate and quite smooth (rare for many MVPs) My only 8X57 I have as of now is my full-stocked Mauser I made for myself a few years back, but I really like it a lot, and I have killed deer elk and antelope with is and just love the way it carries and handles and the accuracy is far better then is should be with just a military barrel (cut down and tapered)
Paper shooting is something I did for years and I was pretty good at it, but I have come to be bored with it, and these days I enjoy field shooting and hunting as much or more then ever, but I no longer shoot in target competitions, so if I were to loose my 308s I would be saddened , but not near as much as I would be if I lost my 8X57. I have also killed elk deer and antelope with my MVP too, but the MVP is a mass-produced rifle I can still buy, and the hand-made Mauser is more dear to me because of the time and labor I invested in making it.
So I think any honest comparison between the 308 and the 8X57 is and will always be a comparison of rifles and purposes the owner of those rifles have, but the 2 cartridges are close enough to overlap about 98%-99% for everything they will do. In other words, it's a matter which you LIKE more but that is usually going to be a matter of the actual rifle, less then the cartridge it's chambered for.
