Played through it nonstop the past few weeks, just finished my third run on Old School. Old school didn't really make too much of a difference for me as I hadn't used the cover system at all my first two run throughs, though I did like the lack of mercy given to me by the removal of last man standing.
Really, really loved it through and through. Game's graphics are awesome, and music is fantastic as well. Gameplay is classic Max, though certainly a little too classic Max in places, as it started to become memorizational bullshit like Max Payne 1's final levels were in the last two acts, though it never gets as bad. Still, aside from those few complaints, the levels were surprisingly well designed, it was the perfect length, and the gunplay is as great as it always was, emphasized by the euphoria engine.
As for the writing, what I think a lot of people here may not have picked up on is that while Max doesn't sound like the Max we're used to, Max sounds like Max should sound given his realization at the end of Max Payne 2 that he needs to move on. In Max Payne 3, he's beating himself up because no matter how he hard he tries, he can't move on. It really is the next logical step for the character.
However, I certainly can understand the sentiment that there didn't need to be a next step, as the bittersweet ending of Max Payne 2 closed the chapter of Max Payne's life that the original game opened. It was a flawless and absolutely perfectly fitting ending, and I see no fault in the argument that there didn't need to be another. Ultimately however, we have to deal with the cards we've been dealt, and I think that in regards to at least Max's characterization, Houser hit the nail on the head.