Based on your game preference I would say xbox.
Hitman and Splinter cell, available, but why not try Assassins creed also? Maybe Tenchu too?
Puzzle games not so much, but the arcade port has lots of puzzle games, I would very much like to recommend one of my fav titles of last year LIMBO, also check out puzzle quest (1), and Hexic (which comes free anyway).
Point and click games sadly I would say have pretty much died :( However there are some games that just about fit that description on 360.
Lost, Sherlock Holmes, Grey Matter (coming soon), Interpol (xbox live arcade), 3 Wallace and Gromit games (XBLA), 2 Sam and Max games (XBLA) and 2 superb Monkey Island games (XBLA).
That said though if you like point and clickers, it might be best searching for them on the pc, as the pc has a wealth of them, or even a Wii.
Both consoles have there upsides and downsides. For example PS3 has its online service gratis, free of charge.. the downside is the online games are plagued with 5 year olds "tea bagging " you. meh.
Also like stated before the ps3 also has the blu ray player built in, and I think a more user friendly environment straight out of the box.
However I would still plump for the 360.