For anime, that would be
Figure 17: Tsubasa & Hikaru.
The plot of that one is that a shy, introverted girl named Tsubasa and her father move from Tokyo to Hokkaido after the death of Tsubasa's mother so that her father can learn to become a baker (his lifelong dream) while Tsubasa enters a new Grade school.
Things change when an alien spacecraft crash-lands nearby. When Tsubasa goes to investigate, she finds an injured alien pilot (who mostly looks human) before both of them are attacked by a monster called a 'Maguar'. While hiding from it, Tsubasa accidentally bonds with a liquid combat suit that helps her defeat the Maguar. Upon separation, the suit becomes a copy of Tsubasa - complete with all her memories - which is stated to be something that has never happened before.
Both the alien pilot and Tsubasa's clone (choosing the names D.D and Hikaru respectively) begin living in Hokkaido (D.D using his powers to make Tsubasa's dad think the two are twin sisters), while the group - later joined by another of D.D's colleagues named Orudina - continue to track down the remaining Maguars that escaped the crash and develop new weapons to help kill them, with Tsubasa and Hikaru joining together into "Figure 17" (the designation for the combat suit) to fight the monsters.
The task is made harder as Earth's environment not only empowers Figure 17 but also empowers the Maguars. Furthermore, when each Maguar dies, it 'passes on' the information regarding its death, which in turn helps the remaining Maguars to grow stronger and into more varied and resilient forms.
Outside of the monster fights, Hikaru and Tsubasa begin to grow closer and even naturally act like siblings - Tsubasa helping show Hikaru the wonders of living on Earth (which is all a new experience to Hikaru despite sharing their memories) and Hikaru in turn helps Tsubasa to grow, in which Tsubasa eventually regains her confidence and comes to terms with her mother's passing.
However, there is the prominent understanding for Hikaru that once their task is completed, she - one way or another - will have to leave Tsubasa and Earth behind.
The episodes are twice as long as normal, which does allow for more character development. That said, there are plenty of both sweet and sad moments, while the finale (without giving anything away) does tug at your heartstrings.
Here's the show's opening (Tsubasa is the one with the hairclips who has a more worried expression, while Hikaru has her hair tied into a small ponytail and has a happier expression):