If you liked
Tengen Toppa Gurren Lagann
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...then you might like
Darling in the FranXX
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I had a hard time getting into Gurren Lagann, I dropped it several times before finally getting past the near vertical learning curve to engage it. Franxx suffers a similar issue, where the writers/producers took a highly artistic approach to the narrative and let me tell you, its FANTASTIC. Most negative comments revolve around the first 6 episodes, where everything makes sense if you keep watching. Do yourself a favor, if you liked Gurren, come to Franxx with no expectations and see where the ride takes you!
If you liked
Shinsekai yori
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...then you might like
Darling in the FranXX
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I was reminded of Shinsekai the entire time I watched Franxx, but not in a bad or comparative way. Rather, the more mature themes of human connection and psychological games were fairly strong throughout. Franxx seemed to convey many similar feelings and messages, in a similar sort of world. Chances are, if you like Shinsekai then Franxx will be enjoyable in a unique but familiar way - though you've really got to go deep into Franxx before it reveals what kind of story it is, its definitely not a 3-episoder - give it, like, 12-14.
If you liked
Kill la Kill
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...then you might like
Sekai Seifuku: Bouryaku no Zvezda
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Lots of humor, crazy battles, interesting story and character development. I found this story to be similar in its scale and world-conquering themes yet equally outlandish. Sekai Seifuku is a bit more reserved and light hearted with far less fan-service but some similarly themed "armor" choices. Similar ideas of conquest and revenge along with changing and proving loyalties show up in each. If Kill la Kill was a bit much for you, Sekai Seifuku should fit the bill.
If you liked
Stella Jogakuin Koutou-ka C³-bu
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...then you might like
Sabage-bu!
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Its similar to the point of bordering being created using the same storyboard. The characters are similar and both have a new girl conned into joining the survival games club. It is also heavily based on action but has significantly more comedy involved.
If you liked
Kokoro Connect
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...then you might like
Stella Jogakuin Koutou-ka C³-bu
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If you wish Yura's character had developed further than Kokoro Connect may be a good option (be sure to watch the extra episodes 14-17 too). In both shows the main female characters go through significant changes causing friendships to be strained. The ideas of forming an identity and personal empowerment are explored in each.