The mistake everyone still seems to be making is that Max Payne 3 is a game...
Jokes aside, I did enjoy the combat, but there were just too many damn cutscenes. You can actually skip them, but not until certain points in the cutscene. I'd guess it's to do with loading times, but even on an SSD, it still took forever - usually over half the length of the cinematic - to get to where I could actually skip them.
In terms of story, I honestly found it boring. Being a huge fan of the original games, and the dark, noir, comic book style, the third game just felt lacking. Max is a less interesting character - instead of being a tormented soul, he's just a depressing drunk, and I never felt involved in what I was doing. You're essentially a freelance bodyguard chasing after some spoiled brats who I wanted to keep throwing out of a helicopter.
I found it more disappointing coming from the first two games with such high expectations than I did a bad game, and would find it hard to recommend when you could pick up the earlier games instead. I actually went back and played through Max Payne 2 after finishing 3, and it was
so much more fun.
One thing I would recommend if you go for it is playing the game on normal. It gives you more bullet time and more health, which means you spend more time diving around like a badass, and less time hiding behind walls.