BD seems a little less open, since it is divided into 4 separate acts, and the goal is more specific (escape, rather than save the world). On the other hand, you can jump to the battlefields pretty much whenever you want. DD could seem a little overwhelming at times (which could be good or bad, depending on your point of view).

The story and humor is similar.
The background graphics are similar. In BD act 1 is indoors and a little dark / gloomy, but it opens up in acts 2 and 3 to to a greater variety of outdoor environments. see; Pictures of BD
The characters in BD are 3D, so there are more customization options during character creation, more animations and more types of equipment, which look different when equipped.

There are more characters in BD, but there are few that you deal with throughout the whole game. Some characters are memorable, but you probably will not get that attached to any.

Since you liked DD, I'd expect that you would probably like BD.