Master Chief is a Spartan. He flips warthogs (the jeep kind) and tanks. His armor has an energy shield, meaning the first twenty bullets, and I'm being generous, don't count. His body has been honed physically and mentaly to be the perfect killing machine since he was a child... and then he had his body enhanced some more through science. He's the classic super soldier, a one man army.
Max has bullet time, extreme determination, a large arsenal, and enough drugs to knock out twenty retirment homes.
Max uses modern weaponry. While Halo's weapons arent that much different that we can tell, we have to assume they have improved over a couple hundred years. Thus his shield should be able to take more of a beating.
Looking at thier acomplishments we can see that MC has torn through an Empire that had nearly ground the humans into dust, while keaping hords of zombie-esque physically enhanced creaters know as the flood from infecting the entire universe.
Max Payne. Not quite as much.
Now, if you look at this from a factual point of view, not with your own bias toward the games or system, Chief edges over max. Its not cut and dry, as it all really comes down to whether MC can weather the blows dished out from Max's Bullet Time... but I think he can.