Thoughts so far:
It took me a while to get used to the setting - I was wondering how they could have anything vaguely film noir or John Woo-ish in a tropical urban paradise. But having sunk a few hours into it I've realized I had it completely backwards. If Max Payne 1 and 2 were homages to the works of John Woo (and to a lesser extent, the partially Hong Kong action film inspired The Matrix), then this film is an homage to the more recent works of Michael Mann like Miami Vice or Collateral. And it actually works fantastically, as it's a logical place for the character to go next. Kane and Lynch have already explored this territory, but their gameplay was so unrefined - and their characters so utterly detestable - that I'm finding it hard to argue that this isn't a much better homage in just about every capacity.
I also think that a completely linear, story-driven game is a way better playground for the Housers to play wannabe directors than an open world game like Red Dead. The pacing is tighter, the tone is more consistent, and the graphical fidelity doesn't fluctuate depending on the complexity of the environment anymore.
Mechanically it's still very much Max Payne - aside from hit-and-miss (mostly miss) last stand system, bullet time and health are largely unchanged. What is killing me is the sluggish analog stick input. Aiming feels... heavy. Sluggish. It's hard to put into words. The aiming is too slow (even with aiming speeds turned up to 10) to feel quite right as a vanilla free-aiming third person shooter. Despite the R* pedigree, this isn't a GTA4 or Red Dead style "lock-on to their torso and then aim for their head" shooter. It's not a COD-style "keep tapping scope to auto-lock your way through" game. It's closer to "Once every few seconds you can hit the lock key, and it will zoom to the closest enemy (whether or not you can actually hit him). Then it will stop locking entirely. Then you need to push your gun through molasses to put an enemy's head under your reticule."
You can get used to it in some areas - especially open combat, where cover and bullet time can negate aiming deficiencies. But other segments that are more scripted require tightly timed responses, and the slow aiming is pretty brutal.
And you can catch yourself up on the story through Youtube or something.