The food is similar in both venues, but the H-D-D is more of a show with audience participation and corny jokes. You are served your food at a table. Mickey's BB is held in the pavilion, so it's almost outdoors with buffet lines and picnic tables. Some have said it's hard to get food for little ones and also get a place at a table. DH and I celebrated our anniversary at the BB in 2003, and loved the characters, line dancing lessons, rope tricks, etc. They announced birthdays, anniversaries and other special dates, and had a special dance for people celebrating an event.
We've had a good time at both.