Well, I've played them all except Sly 1, and my vote would go to Jak and Daxter.
With regards to the first Jak game, I'm somewhat blinded by nostalgia, The Precursor Legacy being the game I got with my PS2 on that Christmas morning 12 (12! - makes me feel a bit queasy thinking about it, though I guess it's nothing compared to NES or SNES kids) years ago. I've beaten the game five times in that space of time and still find it refreshingly fun and lighthearted compared to the games I play now.
Jak 2 is a widely unbalanced game, jumping from easy to difficult and back again with little indication. I can't remember getting as angry with any mission in the last five years as I did with the "escort three guys through the sewers" mission from that game. That said, it can be wildly fun once it isn't tripping over itself. You might even get lucky and breeze through the hard missions on luck alone, as I did two years earlier, when I somehow managed to pass all the hard missions in four attempts or less (and I'm a strictly easy mode player).
Jak 3 corrects all the problems of 2, and wraps up the trilogy's overarching story nicely. I remember having a lot of fun with it, but haven't completed it in years - it's quite a big game, and I don't have the time to search for all the optional trinkets I know I'd end up looking for. It also brought platforming back, which was sorely lacking in Jak 2.
I've only played through Sly 2 and 3 once, and seeing as I bought them cheaply at a much later date, they don't hold the same nostalgia factor for me. I will say that I found the third Sly game suffering from difficulty spikes that were comparable to Jak 2's. By the time I got to the shooting section at the end, I was tired of endless restarts and quit after one death. As such, I don't know how that story ends, but the second's story wasn't great, if I recall correctly. Also contrary to the Jak and Daxter games, each Sly game felt like an improved version of the last game, with less of a fundamental change in gameplay, and more a refinement of a formula.
However if I ignored the difficulty spikes in Sly 3, it would probably be the best game on this list. It's funny, ceaselessly inventive and has a great Ocean's 11 vibe going for it.
I've gone a bit off-topic though, seeing as you asked about the HD collections. I only own the Jak one, and have only played Jak 1 and 2 off the disc. Both look great in HD (especially The Precursor Legacy which is very colourful and bright), and work without any noticeable software glitches. I never tried Jak 3 HD, but I expect the same care was taken with it. Having no experience with the Sly games in HD, I don't know if the same care was taken with their transfer. Maybe a review would tell you that.
When all is said and done though, you're going to get a collection of fantastic games. That said, if I wanted to play as Sly again, I'd personally skip Sly 2 (and Sly 1, by extension), and just go straight to Sly 3, whereas if I wanted to play as Jak, I'd go through all three of his games.