Once you have completed the game with Sora, you will then be able to take part in Riku's tale. This is known as the Reverse/Rebirth mode. This will give you the story, as it unfolds in Riku's perspective. All of the events that happen in Sora's journey, such as the defeat of Marluxia will also happen in Riku's story, as part of teh storyline rather than one of his events.
Riku's story is of his coming to terms with his darkness, and finding his way out of Castle Oblivion.
The gameplay is very much the same in Riku's game as it is in Sora's. The worlds he visits will also be the same, though in a different order. (The exception is Riku does not visit 100 Acre Wood) You will have to defeat the main boss of each world, to clear that particular floor. Riku will also run into several members of the organization, that Sora himself runs into. He will fight the same bosses, and battle the same Heartless enemies. But this is pretty much where the similarities will end.
The first thing you will most likely notice is Riku's card deck. You cannot customize it such as you can Sora's. Also there is far fewer cards in Riku's deck. His deck also changes in each new world he explores. This might seem a bit intimidating at first, but actually think of it as a new challenge. If you have gotten the hang of card fighting, (If you are this far, you should have) then there is nothing to worry about.
Also inside each of Riku's floors, there is only one story line. There are also fewer bosses to fight. You will have two new bosses that Sora does not fight: Ansem, and Lexaeus.
Riku's Map Cards
Riku's Battle Cards