My geologist buddies in Russia carry them as well as Moisin-Nagants for bear defense in the arctic.
Interesting. Do you know if the Russians primarily carry milsurp rifles, or do they also regularly have shotguns around? Are they allowed handguns over there?
To the OP, I would go with the 308 if you're asking this question. The 308 will typically give you better accuracy and ballistic performance, so you'll be less likely to get in a situation where the bear is too far. If you're capable of making a 300+yd shot on game, the 308 will be up to the task.
Of course, if you choose to take your SKS, make sure you get some proper hunting ammo, and make sure it feeds, figure out how accurate it is, etc so you can decide on how close you need to get. Generally speaking, the primary limit to the SKS is accuracy and effective range. The sks has a mix of features that come together to make it a less-than-ideal - the factory sights are not very good, the rifle usually has tremendous slop in the stock, ammo quality (particularly surplus, which you shouldn't be using) is sub-par, and the cartridge itself isn't particularly powerful, which means your bullets drops to 2000 fps by like 120yds and 1800fps around 200yds (which is the minimum velocity for proper expansion for many bullets, although I can't talk to the 7.62x39 bullets specifically).
Long story short, it'll kill a bear as long as you do your part and get close enough for what you and your gun/ammo combo is capable of.