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Both deal with time travel/romance. Both FLs sort of "messed up" in their current life and both plots revolve around the FL changing herself to give herself a better fate
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Both have respective son/daughter traveling back to the past to meet their parent. Very cute and heartwarming child/mother bond is formed. Both also have some cute romance side stories as well!
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Both are female centric dramas, although To Dear Myself is a lot heavier on the heart/they take a more realistic and less idealized viewpoint on life.
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Both have detective work and are fairly fluffy romance dramas. both dramas focus on the romance aspect of things and are rather light.
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Both have detective work and romance. I would say Under the Power is more focused on the detective work whereas Maiden Holmes is more fluffy and focuses more on the romance. Both are very good shows!