Want the REAL philosophy in The Matrix? Play the game, watch the animated short.
It's unfortunate that most of the fairweather people (and I would assume many who fancy themselves hardcore) don't get the whole picture of the Wachoski Brothers' "The Matrix" saga, meaning they've only watched the three films. Or perhaps it's more preferable that the deepest philosophical concepts lie within the series of animated shorts "The Animatrix" and in the video game "Enter The Matrix".
In my opinion, the character of Ghost is the deepest of all, philosophically-speaking, both in his actions and dialogue. In the video game he openly and directly admits his admiration of history and philosophy, and quotes several Asian and western scholars (e.g., telling Trinity when she asks when she can get him a girlfriend, "Like Augustine, I serve a higher purpose...onanism").
And in the short films The Second Renaissance, Parts 1 & 2, the fundamental flaws of man that gave alolowed the war with machines to start - vanity and corruption - are exposed, shedding new light on the assumed theory for the passerby that it was the machines who were the evil being in the war, and they that started it. Quite the contrary - the story goes that machines tried a number of times proposing peaceful resolve and a co-existence with their carbon-based counterparts, which fell on man's deaf and ignorant ears. So this changes the whole context of who's battling who.
I enjoy the reference to famous philosphers and concepts peppered throughout the saga (ships, character names, etc.), but I've also found the most meaningful content in the least-marketed products within the Wachioski's empire.
But maybe therein lies the point.