I missed out on voting, but I'd only seen Serenity and most of Strangelove anyway.
I saw Serenity in the theater when it came out, because the previews confused me until I discovered it was based on a canceled Joss Whedon show, which was enough to get me to see it. Apparently I was lucky because it was only in theaters for like two weeks. Then I had to see Firefly so my brother and I bought the box set. Serenity was good by itself and good enough to get me to see Firefly, but it was much better having seeing the series.
Strangelove on the other hand is its own great movie (although improved by Sellers experience). However, I'm a browncoat through and through, so I would have to go with Serenity.
Although, had I been present for the voting, I might have voted for Strangelove just for the tie...