You ask an interesting question with regards to the 7.62x51 (military designation for .308, basically) or 7.62x39, but the answer actually very much depends on you. Ask yourself some questions.
1) What do you intend to do with the cartridge you choose?
If your primary concern is hunting game, both cartridges will do deer sized game handily (7.62x39 is ballistically close to .30-30 Winchester, which has killed many thousands of deer), though you will get much better range with the longer cartridge. Above deer sized game, the 7.62x51 (.308 Winchester) will start to pull ahead with its ability to handle heavier bullets (up to 180 grains really well, above that, you really need a .30-06 to stay in the .30 cal game).
If your primary concern is dealing with 2-legged varmints, another question arises (it matters in hunting, too, but less from a life and death perspective).
2) Just how far out do you plan to engage targets?
Under 300 yards, the 7.62x39 will do just fine. Freedom42 has pointed this out from personal experience. Beyond 300 yards, the 7.62x39 starts to loose ground, partially because exterior ballistics (you start needing a whole lot of hold over to even get a hit) and partially because the farther out you get, the less you have in the way of terminal ballistics. The .308 is moving a heavier bullet faster from the start (150ish grain bullet at 2700-2800 fps vs. 123-125 gr. bullet at around 2300 fps), so it has more punch when it gets out there a ways.
These ballistics are important when hunting, but deer don't shoot back, so I'd recommend getting as close as possible to ensure a clean kill when hunting.
3) What's the terrain like where you live? Urban? Rural but lots of trees? Rural and lots of open spaces?
OK, this is really an extension of the last question, but it still matters. If you're close enough to through and through a bad guy with your shot, you don't want that bullet going (to borrow a phrase from badmuggafugga) "across four lanes of traffic, over the petting zoo, and through three walls of the "special needs" school before finally coming to rest in Corky's abdomen". Rural areas tend to reduce this concern some, so a .308 is less of a concern in these areas.
In heavily wooded areas, long shots are harder to come by, thus the extra weight of the .308 may be more of a liability than an asset. Open areas allow for longer shots, allowing the .308 to really shine, and showing the weakness of the Soviet round.
4) How much do you want to be able to practice?
If you've determined that the strengths and weaknesses of each round pretty much balance out in your book, this question can become the deciding factor...but not always. I go to a lot of gun shows (we have one about once a month in Tulsa, OK, sometimes twice a month, and this is home of the well-known Wannemacher show).
I've seen 7.62x51mm NATO surplus go for between $150 and $180 per thousand ($175 per 1280 of South African in the wooden crates, but you can't find that stuff any more, either). Indian .308 ammo is usually much cheaper, but you'll rarely hear good things about it. I've never tried it.
7.62x39mm ammo tends to run between $75 and $90 per thousand for the steel cased stuff. In a com-block gun of either the AK or SKS variety, I see no reason to shoot brass cased ammo and at least one reason not to (softer primers in US commercially manufactured ammo have a greater likelyhood of slam-fires in guns with floating firing pins than com-block commercial ammo, which uses harder primers).
You're looking at potentially twice as much ammo for more or less the same price with a 7.62x39 over the .308 Win. In other words, you'll be able to practice much more for the same price. You are
going to practice, aren't
Once you've settled on which round will do the job, then start worrying about what platform to shoot it from. And when you get to the question of "Which gun chambered for <insert cartridge designation here> should I get?" the answer is this: "Whichever one you are the most comfortable with."