Ugh, such a tough choice.
The vast majority of 12 Angry Men takes place in a hot and stuffy jury room. It's a thriller, that's driven by dialogue and a great assortment of characters. The directing is precise and well-crafted, and the entire cast is just perfect, highlighted by some great performances from Lee J. Cobb and Henry Fonda.
Alien is known for its eerie and claustrophobic settings. In Alien, Ripley and other passengers are stuck in space, while a deadly creature reeks havoc. Alien features some great atmospheric tension, and this film provides the perfect blend of science fiction and horror.
It's a tough call, but I'm going with 12 Angry Men. The acting is superior, and 12 Angry Men is still praised as a modern classic. Alien is great, but you still have to deal with the "which film is better" argument, when comparing Alien and Aliens, and this comparison puts a slight dent in Alien's legacy.