 If you liked
Noein: Mou Hitori no Kimi e
|
 ...then you might like
Tsubasa Chronicle 2nd Season
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Both series involves time and dimension travel. Also, the male protagonist in both series travels and battles against his other self to save the girl that he loves.
In both animes, the main girl has a extremely powerful power that is related to dimensions, and has a kind tender personality. both animes are focused in dimensions travelling. Also, the main guy is a childhood friend of the main girl and they´re both in love with each other. In both they main guy has a "other self" from other dimension.