It has been ten years since the last Max Payne was released, so its pretty clear that the game had to change in significant ways. Remedy, the original developer of Max Payne always spent a ton of time focusing on the gameplay an the art style, and not much else. The story of the first Max Payne game leads to an odd satanic worship plot, and the second game had an extremely awkward love interest going on. These games always told their stories in a fantastic noir comic book style, but the story it was telling was not usually all that relevant to the combat, which consisted of a lot of John Woo style slo-mo shooting of guys.
Max Payne 3 certainly maintains the slo-mo shooting bit, but it throws practically everything else out the window. Instead of using noir comic book style cutscenes, the game instead gives Max Payne an internal monologue that he uses to comment on everything going on around him. This works far better for expected, mostly because of Max's extremely low self-worth and rampant alcoholism.
In fact, I've probably never seen a more interesting protagonist in a video game before. Max Payne is a seriously messed up man in this game, and its clear that his experiences in the first two games have completely ruined his mental state. He is an alcoholic and a drug addict, and working as a bodyguard for a family in Brazil.
The game's story feels a lot like a Man on Fire at the start, requiring you to chase after some terrorists that have captured the daughters of your boss endlessly. The story never really becomes all that interesting, though, and Max's internal dialogue is probably the most interesting dialogue in the entire game.
When it comes to the shooting, the game controls much like any other third person shooter on the market. The game still makes extensive use of bullet time, and there are several slow motion sequences where Max will jump off something and shoot a whole bunch of guys on his way down. There are two options when it comes to controlling the game. You can either choose to have the game help you out with lock on, or aim at everything manually. Of course, you'll want to use the free aim as long as you're playing with a keyboard and mouse on a PC.
PC performance on this game is about what you'd expect from a game running on the same engine as GTA IV. Lower-end systems will have a bit more trouble than they probably should, but otherwise it's a competent port that pulls off everything just as well as its console brethren.
If you're thinking about picking up Max Payne 3, you should absolutely go for it. Rockstar has done a great job with recreating this series, giving it a darker tone and making it palatable in today's market without completely losing the things that made it so unique.