Harder thump from the x51 round at pretty much all ranges (unless a super short x51 barrel is used -- down in the 11-13" range with 7.62x51 it looks a lot like 7.62x39 from a standard AK barrel ballistically, if I am not mistaken). The x51 round starts with quite a bit more energy, and the heavier bullets usually employed in x51 mean more retained energy down range. On the debit side, you get more recoil from x51 and it generally requires a heavier receiver and heavier weapon, so the x39 round is likely going to be fired from a quicker handling weapon, be it an AK, vz.58, SKS or whatever.
Most 7.62x39 FMJ ammo is notable for poor wounding potential, considering what it is and such. The standard Soviet M43 load was slow to yaw and unlikely to fragment, making most of the wounds it produced less impressive than the might have been. The Yugoslavs and possibly other people worked on this issue to make a Hague-legal but more damaging bullet design.
7.62x51, by comparison, has never been noted for poor lethality, though it's not the silver bullet that some people make it out to be (usually in comparison to rounds like 7.62x39 or, especially, 5.56mm).