The only game I've played that resembles MP1&2 quite a bit, is Stranglehold. Max Payne was inspired by John Woo's movies and mainly
Hard Boiled (it had many references) so after Max Payne was a success someone thought, hey let's make an actual John Woo game, and they made this, which is basically Hard Boiled: The game. It's not as good as MP1&2 and it has more contained levels where a lot of enemies come at you, but it's a very good shooter nevertheless, with some awesome shootouts and a general gun-firing mayhem.