Having played a good bit more, I'm coming to see and understand the type of game Prince of Persia is. This being the only game of the series I have played, I didn't know what to expect from it.
It's a pretty casual game, very much adventurous and story-driven. The majority of the game is exploring and collecting orbs (I forget their actual name). So it's not exactly the most exciting of games, but interaction with the princess (and thus the story) combined with the generally fun gameplay mechanics makes it a light, enjoyable experience.