Here's my quick summaries of Jak and Daxter, all 4 of them, after playing through them all. (No, I didn't play the racing game, shame on me I know.)
Jak and Daxter: Precursor Legacy - or as I call it, Jak and Daxter: Spyro Egg Collecting Edition
Classic loot collecting platformer. Has a few minor annoying minigames, and difficulty is random, but other then that it's brilliant and a must play on PS2. Lots of classic platforming moments and the moveset you have is both devious and amazingly useful at the same time. I do have one thing to say however, and that is the game doesn't ever tell you that while rolling you can "long jump" with X. (If it did, I must have somehow missed the tutorial trigger.) So just remember that or you'll get stuck about 3/4th of the way into the game when that jump method becomes required to access a new area.
Jak 2 - or as I call it, Jak and Daxter: The Maddening Controller Selling Edition
Really bad GTA segments with really random frustrating timers on everything. Like seriously, everything. Deliver someone to point A and B and C, have a timer. Fight off the enemies, with a timer. Race through rings, with a really short timer that is reset each ring. Did I mention that the hovercars have very little health and that you only have 4 hits(you have 8 health, but everything does 2 damage so I don't see the point really.) The platforming isn't too bad, and brings some welcome difficulty, but then you'll get to a boss and quickly find out that fighting long often badly designed boss fights with 4 health and random, super rare health drops from crates(they would rather drop ammo even when your ammo is full) does not equal fun. Story is good, but not worth the frustration of the gameplay. Oh, and the minigames are hard too, in case you thought they would provide some fresh air.
The big killer though is that checkpoints save your progress(you'll spawn at the checkpoint), but they don't reset your ammo. This means you'll be tossed back into the boss fight due to your autosave(which cannot be turned off), but have to spend the next few runs just grinding for ammo instead of trying the boss fight properly. This is partly because the bosses are designed so that they will often do some cheap hits on you and so you need full health to fight them and full ammo to end the fight quick enough.
It's hard to say it, but this is one PS2 game that I cannot recommend to anyone unless you've got the patience of a saint to put up with all the cheap hits or bad runs you'll have when doing the objectives required to see the story. Skip this one.
Jak 3 - or as I call it, Jak 2: What we were trying to do in the first place
A bit of Jak 2 lives on, the story is a direct sequal to 2, but the gameplay is much improved. Just about everything that causes 2 to be the "Maddening Controller Selling Edition" has been fixed. Minigames now require much lower scores to pass for storyline, health actually gets upgraded and dropped more often, the gunplay actually works even if you can't see the enemy on the camera, and so on. While I died plenty of times, the platforming is much more sane then 2 and a lot more fun to retry, instead of feeling like a chore. One other thing that makes this game much more bearable is that it has lots of checkpoints.
There are just a few minor segments that are pretty difficult, one in particular is near the beginning when you need to race on these dinos that you haven't really had much practice controlling yet(they have a tricky double jump mechanic that makes it tricky to figure out how to move fastest with them). The rest of the potentially frustrating races are reserved for egg sidequests, and not required at all for storyline progress.
Don't get me wrong. Jak 3 is still difficult, and you will probably die a lot. But thanks to the checkpoints and the segments being shorter, or in the case of longer segments, being easier, the game redeems itself from the problems that plagued the 2nd game.
Jak and Daxter: The Lost Frontier - or Jak and Daxter: Sky Pirates Freelancer Edition
First of all, this one suffers from clearly being a port of the PSP version. However, it's still pretty well worth the time to play it once you get over the fact that the graphics are a bit dull and the camera is a bit more "auto-controlled" along paths(probably to make the PSP version easier to play, but it feels a bit weird when on the PS2.
The game still lets you "overwrite" it's camera angles for the most part if you want to, but I did notice that when I did that sometimes it would still try to "rotate around the corner" with the new angle I gave it, which just confuses the player and made me fall into a pit more then if I just went with the normal angle. The normal angles are usually pretty good though, and this issue only plagues the platforming sections of the game.
Most of this game will be spent in the cockpit of a ship, flying around arcade/Freelancer style, doing dogfights or exploring the many small but pretty detailed(for a PSP port) "area map overworlds". Basically each game location has one of these overworlds to fly in, and the platforming section's "landing pad" to get to it's platforming level. The result is a strange but really fun mix of Freelancer/arcade flight fighting and more standard Jak shooting/platforming/puzzle solving.
The platforming puzzles come in the form of different powerups Jak gains throughout the storyline, and often the puzzle requires 1 or more of these special powers to be applied to the level to continue on. By the end of the game, there are a few mind splitting combinations of powers needed to take down enemies or mix powers together for puzzles. But it's never overly complicated and exists mostly to separate areas, provide a break from shooting combat, or hide secrets in the levels.
Every now and then, you'll have to be Dark Daxter. These segments are a little weird, as you wander around some very simple levels as a severely overpowered monster. The combat is easy, as the main mechanic of these segments is that you can save up energy from monsters and then become an invincible tornado(it reminds me mostly of Taz from Loony Tunes, and is hilarious). While in tornado mode you break through stuff, and there is a bit of puzzles from the fact you can pick up different enemies too. Even if you find these segments boring due to being overpowered, they are all rather short and simple, so running through them shouldn't take too long.
Even though this one is clearly a port from the PSP, I still recommend it. The Jak difficulty is still there, but once again the designers were pretty generous with checkpoints. As a matter of fact, there are several checkpoint mid-battle in the Freelancer ship bosses that remember the bosses health but restore your own if you died mid-battle. Little touches like this help ease the difficulty so that the player keeps trying instead of giving up like Jak 2.
In summary, play Precursor Legacy, Jak 3, and if you want more Jak and love arcade spaceship shooting, Lost Frontier. Avoid 2, unless you're a really die hard fan who has the patience to put up with blatantly bad game design.