What is the advantage for some species of birds to have the sexes look
similar and others dissimilar?

if the male is brightly colored, while the female is a drab color
(such as brown or grey), then the male would distract predators,
allowing the female to get away/hide.

a female blending in with the surrounded vegetation would help if the
bird must lay on some eggs. a female ostrich is light brown, and
usually sits on the nest during the day, while the black-feathered
male would need to wait until nightfall to help incubate the eggs.

another reason would be that it's the male who must impress the
female, and so often is very colorful to gain her attention.