By far, the original.

I like both of them, but Adventure is longer.

Sonic Rush was bare-bones gameplay. Though it was enjoyable, Rush Adventure added to it by introducing exploration mechanics and tighter stage design, which added to the replay value of the game. Sonic Rush may be more valuable for it's story, simultaneously introducing and developing our beloved fiery feline, but Rush Adventure has more depth to it's gameplay and a perfectly competent story, introducing us to Blaze's home world. Sonic Rush Adventure is a gem in the Sonic series.