A dragon staff is basically a contact staff with spokes, or discs on the ends that serve to greatly increase the stick's moment of inertia or slow the roll. This basically means, that once a dragon starts rolling, it doesnt like to stop. Stubborn staffs. This has a lot of benefits and some drawbacks.
First, the visual effect of the ends is awesome! Spectators can really see that the staff is rolling, and rotating rings of flame traveling around your body look super cool.
Body roll pathways can be easier to complete with a dragon, because the moment of inertia is so high, the stick will keep rolling, and if you can keep it on your body, it will keep rolling. You wont need as much precision or little nudges to maintain momentum.
This can also be a bit limiting. It is kind of impossible to change roll directions with a dragon without a hard stop and start, which changes the way that tricks like steves work, and it's also harder to fit those dragon ends into tight spaces, and its a much heavier prop.
In conclusion, there are no tricks that one can do with a dragon staff that cant be done with a contact staff, but there are tricks that one can do with a contact staff that cant be done with a dragon. But, the learning curve for body rolls is a bit less steep with a dragon, and they look and feel very cool!