Oh man. This is a fucking hard one. Though out of those choices,
It would be a tie between Max Payne 2: FOMP, and Manhunt 1 for me... I am totally split between those 2...
Max Payne 2. I do not remember when I got this game, I just remember anticipating its release, If I would have to guess it would probably be for PC in early 2004. Well, I pick 2 over 1. 2, it just seemed to be more "there" if you know what I mean. The character connections, and emotional connection to those characters you can truly "feel" from each character. You can feel what the character is feeling, you can think what the character is thinking, in other words.
Manhunt 1. Fuck, I got this game for PS2 around December 2003, shortly after its release I think, this day I own it on all consoles, PS2/Xbox/PC. This, it creates a whole new element and approach for a R* game, horror. To me, this is a true "non-spiritual" horror game, with (at least to my memory) all real elements. You are on the loose, bad guys are trying to kill you, you have to hide from the bad guys and take them down one by one or be killed.
My only gripe about Manhunt, ESPECIALLY 2 (which is a piece of shit), is where it basically turns into an all out gun fight. Then it just goes down-hill.
After racking my brain a little, I would pick Max Payne 2: FOMP as my favorite non-GTA Rockstar game. Max Payne 2, it stays fluent all throughout the game, at no point do I lose interest in the characters or story throughout the duration of it.