I own all three here is an run down:
The first was fun turning into boring,with platforming and puzzles with 3d graphics is more fun than it sounds, but just before the end it is repetitive and long, the final boss fight pretty much ties up loose ends in the story.
The second was fun, but in an different way, with an dystopic city as the backdrop; though
they had new gameplay elements,the story is what makes this one good; also alot of loose ends are tied up at the end of this game.
The third was AWFUL, it did not need to be made, the story is completely out of the blue (seriously it takes place in the desert) and the only good parts are the city sections which are few and far between; ON FOOT. Also the story aside from a few continuity stuff about the precursors; that is what the story should be about, but they pretty much brush that to the side esp. the prophet in the beginning. also all those neat new gameplay machanics in the second one is also brushed to the side to make way for CARS. seriously those cars have the handling of a garbage truck on roller blades and are just as much fun. Between the stupid desert town that came out of nowhere, then expected me to sympthize with them three games in without any other mention of it; and the cars and "vehicle" sections that were way too many and given the spotlight while the good gameplay parts were kinda fitted in there because naughty dog felt "well it was in the last game and we can't remake jak AGAIN this time into a car game even though we get anerisms if jak isn't in a car for at least 3/4 of the game so lets show that jak can still shoot a gun just as good as in the last one"
it was awful. I still beleve that the MUCH better jak 2 was the end and Jak 3 was a bad dream from which jak had after meeting the Naughty Dog staff working on Jak 3