What makes this movie so wonderful is how good a job Robin Williams and Nathan Lane do as portraying loving, dedicated parents. Aside from the amazing soundtrack and the fun antics, it is their sheer goodness as human beings that stays in your head for a long time.
A fun thing to do is compare this movie to La Cage Aux Folles and see how different characters are interpreted differently. The son in the Birdcage is a much more complex character than the one in La Cage, and a lot of the movie is about him accepting his identity. The daughter, on the other hand, is much more of a three dimensional character in La Cage.
The other nice thing about this movie is that unlike in the original, you end up liking the girls parents to some extent. They actually do have a lot in common with the heroes. That isn't true in La Cage, where the girl's father seems to be almost sinister