This is a really tough call, both stinks. But which is better? I guess there are elements in both films that are better than the other. I think the human characters are better written in The Predator. You could see there is potential in how they were introduced...until it all went downhill half-way into the movie. There was such promise...then its like Shane Black suddenly just took a big dump on all those characters. I mean Keegan-Michael Key, Olivia Munn, Thomas Jane, Alfie Allen, etc, are accomplished actors and I felt their talents were just wasted in the latter half of the film.
In contrast, I really could not stand following pizza boy's adventures with his high school crush in AVPR. What the %^^&#@! was I watching? Some crappy teenage drama? Come on. I didn't pay money to watch stupid drama like Dawson's Creek or Berverly Hills 91210. And the dialogue? Oh man.
On the other hand, I kinda have a soft spot for the Wolf Predator in AVPR. I always wanted to see how an elite level Predator will dispatch the Aliens on screen. Part of that is also purely subjective, in how I played Aliens vs Predator game way back in the day, and that bias I have ever since dreaming of an awesome predator. At least on that level, AVPR made my dream come true in a limited extent.
In comparison, I didn't saw anything special about the Fugitive Predator. So he wanted to deliver the Predator Killer suit. That was a kinda cool concept, but not really executed well.
So all-in-all, I think The Predator is objectively a marginally better movie than AVPR. But ultimately it ended up a more disappointing viewing experience for me than AVPR. You could see there was the potential for a good film there, but it just got sidetracked and railroaded halfway into the film and that is such a letdown.
AVPR however, I can see now it had no pretensions to be a fantastic film. It is what it is. A bad movie...but somehow a terrible film I found enjoyable to watch in a guilty pleasure sort of way.