Which is better? Power and speed wise, I guess.

Dragonbone bow is stronger and shoots faster, but is heavier. Daedric bow shoots a bit further though.

I'm pretty sure weight is the main factor in deciding draw speed for bows, actually. That's why Bound Bow is one of the best weapons in the game.

Before I got Dawnguard I used to use the Deadric bow all the time, the I swiched to Dragonbone. I can't tell much of a difference truth be told. If I went in with a stop watch maybe, but I'll go with the cop out answer and just say use what looks nice to you.

Dragonbone.

I am 100% certain that the Dragonbone bow weighs more and draws faster than a Daedric bow.

dragonbone is stronger...but I like how the daedric bows looks. It's so badass