Did you search for other threads on this question? There's another one right here, for example.

I never considered the HD as it's just physically too big for my tastes. As it has a bigger screen and smaller battery I'd expect the HD will have worse battery life if anything. It does have more app storage though - if you want to install a lot of apps and don't want to get into rooting then that's a point in favour of the HD. Have never listened to music on the HD - on the Desire it's fine via headphones (especially if you install a decent music player), you wouldn't really use the speaker for music though.

 

SLCD screen and better processor actually means battery life is comparable with the Desire. Size is the main thing and it is quite large but I had an HD2 and got on fine with it

 

Desire is SLCD as well these days.

Really the OP should try handling both and see which (s)he prefers. To my mind the size and internal storage are the most important differences.