Dug out my Xbox copy of Max Payne 2 (that's a lie, it was on the shelf beside me).
Haven't played it in about twenty years.
Tried it in both my Xbox and 360.
Visually there's no difference, so the 360 emulation is a perfect match (360 emu is supposed to add MSAA to OG Xbox games, but it doesn't do it with all titles. And I couldn't tell in this case). Performance seemed more erratic on 360.
Compared to what John showed on the PS2, the Xbox version has significantly more detailed textures, lighting, and geometry. It has cutbacks to scene complexity, however, just like the PS2. Fewer objects, no mirrors, etc. The aiming on the Xbox version seems rather poorly-tuned (I remember that aspect pretty well). I don't like the "Fast Aim" button click instead of just giving Max a faster camera speed all the time. It's pretty clunky and hard to control.
Ultimately, there's no real reason to ever play Max Payne 2 on Xbox or 360 if you have an Xbox One or higher, since it's backwards compatible and much better on the new systems.
(the one expection being CRT support on Xbox/360)