The Matrix is one of those sci-fi epics that totally envelopes you into its wholly unique story. Its intent seems to be centered on blowing your mind; for most I'd say it succeeded. Badass ninja-style martial combat? Check. Badass gun scene? Check. Implementation of godmode and superpowers? By the end...check. The film gets tainted by its sequels quite a bit, as they try to over-explain plot mechanics the Matrix never intended to travel. Much like Star Wars gets tainted by the newer trilogy, and its over-explanation of the Force, and how it works. The greatest thing about the Matrix - and in kind, the original Star Wars trilogy - is they built this universe totally unapologetic to anyone. For two hours, we lived in it, but they never quite got into the finer details of how everything was possible. And when you're dealing with concepts that Matrix charges head first into, that's important; same reason I really liked Looper. There's no need to tackle the bigger "where did it all come from" and "Matrix inside of a Matrix" bullshit that 2 & 3 take on. So in its chaotic simplicity, the original shined.
The Sting is still a better movie. I just wanted to give a great sci-fi classic its due. Paul Newman and Robert Redford put on a performance better than anybody in the Matrix. In fact, most of the stars of the Matrix aren't very good actors; some border on being awful. You will never be able to make a legitimate claim like that about anyone in The Sting. It is indeed a period piece that clings to its subject material better than most of its kind.
I'm open to hearing arguments from the opposition, but I'd be really surprised if anyone could convince me the Matrix was a better film than The Sting.