All 3 games are great in their own way, but for me AvP 2 hands down is the best.
It's the closest thing to perfection I can think of, it captured the true magic of the classic Alien & Predator films & seamlessly brought them together into one epic universe. The Marine & Alien campaigns really felt like you were playing through Aliens, with the mood, sound effects & visuals all paying great homage to the film while expanding on it at the same time. The Predator campaign also blew my mind when I first played it, those first couple of levels in the jungle really made me feel like the original 1987 hunter stalking its prey from the treetops.
Another thing I especially liked was that there were so many of the original movie sound effects in the game. From the gutteral throb of the Predator's vision modes to the sound of its iconic roar & plasma cannon blasts, it was all taken directly from the film, which added that extra level of authenticity. The same goes for the Alien sounds as well.
On top of that all 3 campaigns were very distinctive & captivating. Unlike AvP 2010 you weren't constantly just running through the same levels with a different character, each narrative was completely unique which made the overall experience feel much grander in scale. AvP 2 is a 10 year old game that I can still play today & love every time I go back, it has far greater replay value than either of its counterparts. As far as crossovers go, you can't do it any better than this.