I won't vote. They match each other in too many achievements - acting, directing, score, mood and perfect pacing - no fat at all. They're two of my favourite fims ever and imo as near flawless as they come in aim and execution. I still watch them regularly with utter absorption and admiration, and still find them to be benchmarks in horror film production (I think the "horror" label they get can perhaps distract from their achievements in accomplished film making though)
Like I said, I won't vote, but if the edge
had to go to one, it might be to Alien.
There's something I find both deeply thought provoking and extremely unsettling the moment after they wake and discover they're way off the beaten track and a long way from home. It's that feeling that anything that has ever meant something to you, people, places, memories, human history, is so far away hidden somewhere in the vastness of space that all you knew may as well just be a strange dream, and the experience would be a terrible lamenting loneliness if dwelt upon.
Charlie, I can't agree with you on the Aliens over Alien (or The Thing) score. For starters the Nostromo design smokes the Sulacco

But maybe for another thread huh?