Finally, an excuse to use my Tohji icon!
I don't really think you can compare Evangelion and Watchmen. Yes, they're both infamous deconstructions of semi-culture specific stories. (Although by this point, I wouldn't really say Mecha or Superheroes are as Japanese or American as they once were.)
That aside, they're very different stories which focus on entirely different things. I adore them both and consider them some of my favorite stories, but I don't think they have much in common.
In a technical sense, I would say that Watchmen is the better of the two, hands-down. It's more consistent, its story, characters and message woven much more tightly together than Gainax's.
Yet... Evangelion had more impact on me, emotionally, and not just because it scared the shit out of me as a child. (I first saw bits of it when I was 10.) I wouldn't say that Eva's message is better than Watchmen's, but that it is directed to everyone, rather than a somewhat specific time. (Watchmen certainly has messages for all of us, but it's also quite clearly directed at an 80s audience.) In this sense, despite Evangelion's many flaws, I would say it is the better story.
But ultimately, I can't really make the call. They're both great stories but I don't think one is better than the other.
Although now I kind of want to see a crossover, damn you.