 If you liked
Macross F
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 ...then you might like
Sidonia no Kishi
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Both feature life in space on a huge ship, both have an ace pilot protagonist with several supporting female characters fancying him. Both offer powerful sci-fi storyline touching various sci-fi phylosophical questions.
Note that Knights of Sydonia is dystopic, thriller seriers while Macross Frontier is utopic adventure.
The premise of these shows are similar. Humans living in huge spaceship/ships because an enemy have destroyed thier home. Both are also using giant robots to fight this said enemy.
Mysterious, powerful aliens seek to destroy humanity, who has taken shelter in a self-sufficient space colony. The main characters pilot mecha, capable of releasing explosives and lasers, in order to protect their only home and fight these alien creatures.
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Recommended by bunny1ov3r
Very similar, where the alien life form seems to adapt, and everyone lives on ships.
Its like Macross minus the singing
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Recommended by MushroomSage
The two anime have a very similar feel, probably since they are both space mechas with a lot of action. Both anime feature a special pilot as main character.
The major difference lies in the singing