Birth by Sleep is actually my second favorite Kingdom Hearts game. (It's better than KH2, in my opinion.) The biggest minus is the fact that you are basically playing the same story three times, and while there are enough differences to keep you interested, too much plays out exactly the same. I absolutely love the combat system; I think it's the best yet.
But the best thing about it is the story and characters. You get a lot of backstory in this game, which casts new light upon the events of the first KH game. Also, there are a couple really great cameos from some familiar Kingdom Hearts characters which those who have played the other games will enjoy.
For a handheld game, it is terrific. The various worlds' environments are simplistic compared to the console KH games, but they get the job done.
My favorite Birth by Sleep character is probably Terra, and his story had the greatest emotional impact in my opinion. (But if you play the game, don't try and save the best for last. Play Terra's story first or the ending will be ruined for you.) Also, Leonard Nimoy's Xehanort is an awesome villain.
Anyway, if you've got a PSP and you like Kingdom Hearts, Birth by Sleep is a solid game and a great entry in the KH story.