It's unfortunate but Max Payne 3 is not a good game. It's a mediocre game. And for a few reasons that are easy to spot but I assume difficult to fix, because they shipped the product with them. And it all boils down to the animations vs controls when shooting.
Your suspicions about the quality of the shooting creep up on you very slowly as the chapters progress, but as the difficulty ramps up throughout the game, and they throw increasingly large hordes of dudes for you to shoot in the face in slow motion, and they push the shooting system to its limit, it unfortunately doesn't hold up.
It starts with noticing that the animations have that GTA IV feel of taking a little too long sometimes. Max doesn't feel spry like in Max Payne 1 and 2. He feels a little heavy like any controllable character from a GTA game. You do a shootdodge, land on the ground then realise that you're hitting the up button on my keyboard and Max Payne is taking FOREVER to get up, then boom while he took forever to do that, you're dead. Then realising that Max has a dedicated animation to take painkillers while in cover that interrupts the shooting even in slow motion. On the face of it it makes sense because Max is hold two guns, he has to stop shooting to put down a gun to take the painkiller. But it interrupts the shooting. The animation priority over the controls pops up in situations throughout the game like this constantly. He just feels too heavy and not responsive enough.
Those are minor problems though right? I'll just power through. But then they start up-ing the ante and more and more enemies start coming in. Then after a while you grow apprehensive of executing on the standard Max Payne style formula to deal with combat arenas. Max Payne is anti-cover based shooting. Instead of hiding behind that box and picking guys off, I dive around or over that box, and in slow motion, look around, scope out the scene, figure out the order i'm going to shoot everyone in, handle that like a boss, all before hitting the ground. And if I miss a few, I pop back up and just shoot everyone off again in slow motion. You become the choreographer of your own personal shoot out scene in your head.
But as the game progresses, and they start throwing more and more stronger armored enemies, who don't die in a few shots, that becomes near impossible. You become more and more apprehensive about shootdodging because Max just won't get up fast enough when there are a dozen guys all shooting at you while you lay there on the ground. And your bullet time takes much more enemies to kill in order to reload, than it did in previous games. Add that to the sheer number of enemies that they throw at you and you will die repeatedly to the point of frustration.
And that's the problem with Max Payne. You won't get to feel cool. You won't get to feel like that choreographer. Instead you'll die over and over until the game takes pity on you and respawns you at the checkpoint with a free painkiller. Then you have to die a few more times until they give you a second one. Rinse and repeat until you get six painkillers then maybe you will be equipped to handle the shots to the face taken while trying to be dive in the air shooting like an action hero. You'll just have to work too hard to get good at working around the shooting system which does not fully equip you with the task you'll be faced with. Eventually that warehouse full of dudes will go down, but instead being like "Yeah!", you'll be like "jeez that was frustrating, when will this be over?"
And I didn't mention the bugs on the PC. The random crashing. A weird bug where Max'll get stuck to cover unable to move, until I reset him by doing a roll with the controller, before switching back to mouse and keyboard. That's when I found out that Max has additional moves like a roll that's assigned to the A button on the controller, but was not introduced with a corresponding button on the keyboard. How is that fair?
What makes it mediocre and not bad though is all the niceties of it being a Rockstar game. You get nice graphics. All the slick, flashy production value in the cutscenes. The setpieces are worth the price of admission. They aren't appropriate to Max Payne by any means, but who cares. This is Rockstar's Max Payne, not Remedy's. It might as well be a whole new thing.
But the shooting is the dealbreaker.