Macross F, Cross Ange: Tenshi to Ryuu no Rondo Recommendations
Cross Ange is actually quite different from Macross F in its basic storyline, if you look past the obvious mecha and romance subplots, but the themes explored are similar. The idea that people are free to choose their own destiny, that people who we conceive of as different and as the enemy may be remarkably similar to us and that music can transcend boundaries are effectively used in both anime.
Some of the characters are also similar. While I definitely preferred Ange, the male MC 'princess' of Macross also displays the characteristic stubbornness, ambition, recklessness and disregard for authority that I liked about Ange.