In the U.S., until the federal government recognizes same sex marriages, there will continue to be a difference in the rights enjoyed by heterosexual married couples and same sex married (or civilly joined) couples. However, it is true that in those states which allow same sex marriage, both groups have equal status in the eyes of the state. The problem with civil unions has been that those states which have allowed them have not extended all the rights of marriage to same sex couples, probably more through oversight than intention.

That said, hurrah for NY state for striking a massive blow for equality.