Max Payne 3 drops below the other two in my opinion due to a broken build (the seemingly endless non-skippable cutscenes - fine for a first playthrough but death to replays), lack of gameplay fluidity and freedom (though it's still pretty damn fun), lack of modding, thoroughly un-Max-like dialogue, poor supporting characters and a story with little personal relevance.
With all that aside, it looks gorgeous, James McCaffrey gives his best performance of the series, the animation is spectacular, Max's state of mind is almost palpable with the Tony Scott visual style, and while the gameplay is very different to its predecessors it's still great fun for what it is.
1's story might be daft, but it is enjoyable. The versatility and definition of the arsenal, variety of enemies, narrative focus and generation of effective new characters make up for Max Payne 2's very few shortcomings, too.
2 is within a gnat's whisker of being the perfect game as far as I'm concerned. And while Timothy Gibbs initially caught a lot of flak for being too different to Sam Lake, I think he captured the visual of Max as a gritty noir hero better than anyone else has. He also somehow manages to match James McCaffrey's voice better than James McCaffrey does.