Depends on your tastes and preferences. First of all, I'd recommend the Ratchet & Clank HD Trilogy
over either of those. I'll (not) briefly profile all three to give you an idea. Sly Cooper trilogy
- Platforming games with a stealth bent. Neat little mechanics for twisty-flips onto points and rails, pick-pocketing skills, and other sneaky techniques. The first game has five zones, consisting of narrow stages between a larger hub, while the second and third games are both 6 or 7 self-contained open worlds with occasional action set-pieces and specialized boss fights (racing stages, etc.). The first game has you controlling only Sly, while the second and third games have multiple playable characters with special abilities. Each of those mini-worlds in Sly 2 and Sly 3 have a fun mix of surveillance, stealth, and combat as the starting tasks in any new area, followed by one or two heist missions that spin delightfully out of control. Sly, Bentley, and Murray have a fun best friends dynamic going on. My favorite in the trilogy is Sly 2: Band of Thieves. Jak & Daxter trilogy
- Platforming games with an open-world bent. The first game is a big ol' collect-a-thon, with finding a total of 1000 Precursor Orbs and 100 Power Cores the major conceit of the game. It's a gorgeous, interconnected open world, but it's more similar to Mario 64 than any other game on this list. I think you need 60 Cores to unlock the final stage, but getting all 100 unlocks the best ending and sets up Jak II. Jak II and Jak III are totally different both in setup and tone - they take place in a dystopian setting where Jak has aged several years and has become a grizzled freedom fighter (...really.). Heavily inspired by GTA III's open world, both Jak II and Jak III are about navigating this new space (and finding bunches of Precursor Orbs, of course) and defeating enemies with a collection of firearms and energy weapons. They're good, and the story has a pretty satisfying arc, but after I played II and III I missed the more colorful, innocent arrangement of the first game. Also worth note: the characters in the Jak universe are solid as a group, but HOLY **** Daxter gets annoying. Something about Max Casella's voice work, man. My favorite in the trilogy is the original Jak & Daxter. Ratchet & Clank trilogy
- Platforming games with a shooting bent. Ratchet games probably have the least-impressive stages in any of these three series, but the combat is HUGELY entertaining, with each game amassing an increasingly ridiculous selection of guns for Ratchet to equip. The first game has the most jumping around and platforming, while the latter two games focus more on the firefights and weapon upgrades. The Ratchet games have the most minigames and alternate play modes of any of these series, with each game having at least one hacking minigame, multiple rail-jumping stages, specialized horde shooting stages, and Clank stages that are more focused on puzzles. I think that Ratchet has the best shooting and overall variety of these three series, but there's almost no stealth and the environments aren't huge and impressive like Jak's Haven City. My favorite in the trilogy is Ratchet & Clank: Up Your Arsenal. Common themes
- Each of these PS2 games were made by a west coast American developer trying to refine 3D platforming from the previous generation while creating appealing, marketable characters and worlds. There is interplay and cross-promotion between all three different series, as the three studios passed some code and assets between one another (for example, the credits of each Ratchet game have Naughty Dog and Sucker Punch in the credits) and shared SCEA as a publisher. There are always blatant attempts at cartoon humor in these games, which is a mixed bag. Generally, these aren't stories to be taken seriously, but each one is respectful to its own mythology enough that there are connections to be made between each game. In all three series (especially Ratchet 3) you can get some bonuses for having completed save files of the preceding games.
Look, I have played a TON of platformers over the years. I am bad at them. I don't always even finish them, and I never collect everything. I rarely beat them with a completion rate above 70%. But all three of these series were a major part of my teens and early twenties and I will always step up to bat for them. Platformers with RPG elements; what's not to love?