I love both movies. But Wall Street has one scene that is truly memorable. One character. Die Hard is legendary as a whole. In fact, it was my original choice for the Number One seed in this bracket. John McClane and Hans Gruber fighting it out in a 36-story building gets my blood pumping every time. Every character in that film is enjoyable. Wall Street on the other hand, suffers from one of the worst casting decisions of the 80's. It has one major fault, but BOY is it major. Daryl Hannah is so clearly out of place so obviously having trouble in her role, that you honestly feel sorry for her watching it. It's not so much that she does a horrible job acting, it's that she does not fit the role. Oliver Stone came to realize, the cast and crew came to realize it, and honestly, that probably didn't help things either. The only other time I have had to skip scenes in a movie due to one character is Aunt May in Spider-Man 3.
Holly Gennero, however, is exactly what Die Hard needs; she's not a damsel in distress, who can actually tries to do something about it. How many action movies before Die Hard, was there a tough woman in it, without her being a trained agent or a villain?
And that's not the only thing Die Hard innovated. Before Die Hard, the 70's and the 80's was dominated by either all out violent action films with all attitude and no humor, or buddy action comedies that went from all out comedy in one scene, to action the next. In my honest opinion, Die Hard was the first good movie since Butch Cassidy and the Sundance Kid, to properly incorporate humor and action together into one fluid film.
And finally: It actually has a plot that makes plausible sense. Most "evil geniuses" plans don't actually make sense, whereas Hans Gruber actually has a plan that could work in real life. I'm not saying that Wall Street's plot is convoluted, because it's not, but there are points where Oliver Stone has to dumb down the plot in order for the audience to understand it, because the movie is almost too smart for it's own good.
My conclusion; both movies are great, but Wall Street has one too many holes it can't cover up, whereas Die Hard has no real weakness.