Sands of Time had dazzling acrobatics, tests of timing, and great room-based puzzles. Warrior Within also has these.

Sands of Time had simple, fairly uninspired combat. Warrior Within has a deeper combat system with more abilities and moves, but still has room for improvement.

Sands of Time had a compelling and interesting story. Warrior Within has an interesting story, but also pokes some holes in itself.

Sands of Time had a very moody (good) soundtrack. Warrior Within has a very angry (bad) soundtrack.

Sands of Time had a spectacular presentation and good graphics, but fairly non-diverse environments. Warrior Within has better graphics and cool environments, but the presentation tended to agree too much with the soundtrack.

Sands of Time had some glitches signifying that the release was slightly rushed, specifically with camera movement and collision with certain objects. Warrior Within has more of these same glitches, and also has occasional fun messing up during mission-critical moments, e.g. time reverses for the Prince but not for the breakaway platform he was standing on.

Summarily, Warrior Within has some good components, but is not a great experience. It's certainly playable, but there are some mistakes that perhaps unduly impact the experience of enjoying the game. I really hope that PoP3 swings back toward SoT, but they say they're going to work even more on a combat focus, so, I don't know.

And if you want to learn what happens in Warrior Within without having to endure playing through it, you can go ahead and watch the cutscenes.