Vampiric Link on opponents creature
Vampiric Link says:


  Whenever enchanted creature deals damage, you gain that much life.


"You" on a card refers to the controller of the card - and regardless of what Vampiric Link is enchanting, you (the person who cast Vampiric Link) will always* control it. So you'll always be the one gaining life, not your opponent.

*barring any control changing effects that occur