 If you liked
Tenkuu no Shiro Laputa
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 ...then you might like
Kaze no Tani no Nausicaä
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Both by Hayao Miyazaki, but these two have keepers of peace that fight against darkness. Just beautiful...
Both of these movies feature strong willed female protagonists who you may think weak at the beginning but prove to be unpredictable. Both have the Studio Ghibli charm and will not disappoint. They are older movies and the animation style is similar. If you like movies that deal with the concept of "man vs. nature" you will be sure to appreciate the depiction of the impact humans have on the surrounding world and how we can create not only chaos but occasionally unseen beauty as well.
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Recommended by xsunshinexo
Their similarity revolves around a mystical/magical/scifi world, made by the same studio and with similar art style and atmosphere.
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Recommended by SeekingWaylander
Both movies are directed by Hayao Miyazaki and both have an environmental preservation beautiful message.
The first two Ghibli films ever made. They both feature the typical strong willed female protagonist, the same Ghibli artsyle and some amazing tracks here and there by composer Joe Hisashi. Both feature two opposing sides trying to achieve power, while the female hero tries to achieve peace between the sides. Both have some amazing action sequences here and there. I recommend Nausicaa to people who loved Laputa. Although I disliked the latter, I do believe both are very similar to each other.