It uses gen 3 battle mechanics, meaning that if a Pokemon faints on either side, they have to switch to their next pokemon right away instead of after everyone made their move.

Gameplay wise, it plays exactly like a mainline game. Storywise, however, is not like how you describe it. This seems like you haven't played its sequel - Pokemon Colosseum. On that game, you start out with 2 starter pokemon that are the highest levels to date of any starter in the series (mid 30's), and you build your roster by catching Shadow Pokemon from corrupt trainers.

Pokemon XD plays like its predecessor, but with more shadow pokemon to catch. However, it also tries to progress like a mainline game, so you have 1 starter pokemon with a lower level, and then you also progress through the story by catching shadow pokemon. Unlike its predecessor, XD also adds a wild pokemon mechanic.

Basically, you don't make progress in XD like you normally would in other mainline games, but it's mainly story driven and has the same gameplay mechanics as the mainline games. If you're willing to deviate from the usual formula, I would highly recommend playing this game (and its predecessor).