This game is much less cheap than Max Payne 1 in terms of how enemies are placed and how they react to you, and the gunplay which was already great in the original game is honestly five times better, mostly due to improvements in physics. Enemies ragdoll in over-the-top ways when killed, and explosions make environmental objects fly into the air, which is just what Max Payne needed to perfect that stylish John Woo action. Everything feels much smoother, movement is less restrictive, and it's still an absolute blast to play today. The gameplay has hardly aged a day, unless you're someone who needs collectables and achievements to enjoy yourself. The story is more complex, has better writing, and is a little less cheesy, but still retains the humour and light parody of the original.
The graphics were improved a lot, and characters have real faces that make better looking expressions than just "neutral" and "constipated". Obviously the visuals aren't great now in a technical sense, but it still looks fairly aesthetically pleasing, which I really can't say about the first game. The art style stayed the same in all the ways that matter; the graphic novel segments look better than ever, and are still the perfect way of telling this story. It's a little less dark and gritty than Max Payne 1 though.
One complaint: Though the first game is very difficult, this one actually went too far the other way, because it's a little too easy until you're nearing the end of the game, which is kind of a shame. Otherwise though, it improves on its predecessor in pretty much every way.