Well, I am admitting my bias to Predator. I care more about the attention given to the Pred rather than the attention given to the Aliens, so I've gotta go with AVPR.
The Wolf Pred was just so much cooler than the Preds in AVP. The AVP preds looked clunky and hokey and the whole teaming up w/ the girl was so corny ... even if it was something that took place in an AVP comic. The AVPR Pred's design was way more badass and more like Pred 2 or Pred 1. And he was just awesome, had awesome technology and was very skilled, etc.
I also just think atmospherically, AVPR was more on the money, it was dark, bloody and all that good stuff.
The one thing I will day is the first AVP had a very interesting plot, but it just fell too flat. The Preds didn't do well and the acting was bad.
AVPR also had bad acting, actually worse acting than the first AVP, but the atmosphere and how awesome the Wolf Pred was give it the edge for me.