If you liked
Ginga Kikoutai Majestic Prince
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...then you might like
Aldnoah.Zero
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In both anime, humanity is at war with another, more advanced species of humans. The "advanced species" in both series has a similar hierarchical society. Both are quite generic mecha shows so they have a lot of other tropes and clichés in common as well.
If you liked
Getter Robo Āḥ
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...then you might like
Terra Formars
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-Similar art -Humanity fighting against a species of advanced bugs -Over-the top action -Manliness -Sci-fi
If you liked
Shinseiki Evangelion
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...then you might like
Digimon Tamers
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Well the psychological themes are very similiar. Also, the final enemies in Digimon Tamers, the D-Reapers are VERY-VERY similiar to Angels in Evangelion. The last D-Reaper even has a mask like Lilith did and it's face evolved to a human's one just like Lilith's .. While Digimon Tamers isn't that sad, psychological and fucked up and is targeted more at kids than Evangelion then it's still clearly influenced by it. Also, in both series there is a company that is related to the D-Reapers/Angels. And some of the digimons in this series are based off the Evangelion mechas. (one of them even had that big wire thing coming out of it's back)