The best shooter games like Max Payne 3 are Max Payne 2: The Fall of Max Payne, Vanquish and Red Dead Redemption 2. Below are 7, each with the reason it is here — and, at the end, what filtering to shooter costs you.
Filtering to shooter means you want the guns to be the answer. It is the right filter when what you liked was the feedback — the sound, the recoil, the way enemies react.
What you get: Moment-to-moment feel, and the shortest distance between picking a game up and enjoying it.
What made Max Payne 3 worth playing in the first place is covered on the full list. This page is the shooter part of that answer, and only the shooter part.
The noir the third game left behind, and the tighter story.
The same commit-and-slide idea at three times the speed.
Rockstar's other shooter, with the same animation weight.
Bullet time plus the best shooter AI anyone has written.
Sliding, wall-running and bullet time in a small sharp package.
Third-person combat with the same physical weight to every impact.
The heavy cover shooter of the same generation.
Variety. Shooters commit hard to one loop, and the ones that try to be something else usually do the something else badly.
Specifically, these are strong answers for Max Payne 3 that are not shooter games, so they are not on this page:
The full list is on games like Max Payne 3 — 9 picks, no genre filter.
Max Payne 2: The Fall of Max Payne. The noir the third game left behind, and the tighter story.
No. Max Payne 3 released on the PlayStation 3, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
How the guns sound and how enemies react to being hit. A shooter with mediocre levels and superb weapon feedback is more fun than the reverse, every time.
Each pick says. Several of the best shooters ever made are single-player campaigns, and a few of the co-op ones are genuinely worse with bots.
By hand. Each pick was written for the full Max Payne 3 list first, on what the game actually does, and this page is the part of that list that is shooter — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the shooter guide for where to start in the genre generally.