Hmmm, just to be sure, I thought I'd double check. The AVP craze started in Dark Horse Presents #34 which featured an Aliens story where the Alien Queen was on a predator ship. This was November 01, 1989. It was an Aliens story but it was the first chapter in the first Aliens Vs. Predator series.
https://www.darkhorse.com/Comics/91-166/Dark-Horse-Presents-34The story was continued in Dark Horse Presents #35 in December 1989. This was a Predator story, but if you look closely, you can see an Alien head mounted onto one of the Predator character's chest armor.
https://www.darkhorse.com/Comics/91-167/Dark-Horse-Presents-35The first actual Alien Vs. Predator confrontation took place in Dark Horse Comics Presents #36 which was the culmination of the 3-part run in Dark Horse Presents. This issue came out in February 1990.
https://www.darkhorse.com/Comics/91-168/Dark-Horse-Presents-36(These 3 Dark Horse tales were eventually reprinted in Aliens Vs. Predator # 0 on July 01, 1990, and of course subsequently in the Aliens Vs. Predator TPB)
https://www.darkhorse.com/Comics/91-043/Aliens-vs-Predator-0-of-4Man, that seems so long ago. Nobody even really heard of Nirvana or Kurt Cobain back then. No Oasis, no Spice Girls, no Brittney Spears, no Alien 3.
But the official first issue of Aliens Vs. Predator came out on June 1 1990 (ahead of #0)
https://www.darkhorse.com/Comics/91-044/Aliens-vs-Predator-1-of-4According to IMDB, Predator 2 premiered in Westwood, California, on November 19, 1990. So, the series definitely started in the comics.
http://www.imdb.com/title/tt0100403/releaseinfo?ref_=tt_ov_inf+It was apparent that the authors at Dark Horse were trying to create a story with loftier goals than the Predator movies on their own, but although the AVP stories in the comics were great, I just don't think that their quality was quarried through into the films. There can be no loftier questions in life than where do we come from?, or what is our purpose? For better or for worse, the Alien series tries to tackle these questions. Although, one can't expect to find the meaning of life in Hollywood horror / sci-fi, the speculative nature of the Aliens series makes it more fun. Every mystery solved, unearths another mystery. But everyone is entitled to their own opinion. I love the Predator films too, but its just a different kettle of fish. I think RakaiThwei said it best, Alien is like a fine wine, and Predator is like a great beer. It's ok like this. Beer's great too...