When I was a kid I had Sonic Rush, while my sister had Sonic Rush Adventure. We would trade between the games, so I would get little snippets of this one. I never played through it until now, however.
It's fast, hyperactive sonic fun, with clever level design. The boost mechanic carries over from the first game, and it works REALLY well. Like all sonic games, you get a sense of invincibility when you are going fast, until (sometimes weird) enemy placement forces you to pump the brakes. Hardly the best platformer on the DS, but you shouldn't overlook it either if you dig the Sonic formula.
Main complaints is that the story doesn't explain itself too well, but I wasn't exactly in it for the story, so that's alright. The music is another complaint. I might be asking too much for it to compare to the first Sonic Rush game, but I found it a little underwhelming. The tunes are catchy, don't get me wrong, but they feel like a pale imitation of Hideki Naganuma's work on the original.