Fantastic Children

Very similar plots, pacing and characters. They both had a similar atmosphere. They each can be rather dark and serious. 

Noein is like a jazzed-up version of Fantastic Children. A group of mysterious people have something to do with other dimensions, and they get involved with some kids, including an important girl they are looking for. Some of them give up on the mission along the way; there's sci-fi, and mystery (and other related things that might be spoilers). They're both somewhat mature series, with lots to think about, and some quiet yet vivid drama, and they don't have a lot of action or romance. Have a somewhat unusual art style. Incidentally, they are both original series (not based off anything) which may be why they both have a strong cohesiveness throughout the whole. read more 

Noein and Fantastic Children both plays on the science fiction theme with its futuristic setting. They come with a package of characters. Their setting not only focuses on a setting in the future but also revolves around dimensions that unlocks mysteries to answers. Important characters are introduced throughout both series as the character seeks what they are looking for. Both series also contain action, drama, and romance with minimal amount of comedy. 

Both have scientific qualities to the plot, as well as mysterious people in black creating disturbances in our 'normal' world.  

Both series focus on groups of enigmatic black-clad beings taking part in inter-dimensional and scientific affairs that are initially unknown. Running alongside said scientific stories are young children who have bigger connections to the groups than what is immediately apparent. These stories with the children provide key emotional moments and give the characters connections with the group. Both shows also have difficult lexicons to understand, with full attention required to get the best out of the stories. Additionally, both soundtracks are absolutely beautiful. 

Both deal with reincarnation within a fantasy/sci-fi setting as their primary premise. 

Both series deal with people with a tragic past, reincarnation, and alien life forms in a science fiction sense. 

Both Please Save My Earth and Fantastic Children are both sci-fi series that deal with the theme of reincarnation of the main characters from lives past and how it affects them currently. They both have their own takes on things, Fantastic Children involves more fantastical science concepts while Please Save My Earth involves more psychic powers, but they both have the similar reincarnation theme. If you watched the Please Save My Earth OVA and you were upset at the blunt ending, Fantastic Children should serve your needs well. If you read the Please Save My Earth manga and want something similar, try Fantastic Children. 

Scientists group from another planet reincarnate in our planet. Please save my earth is a shojo, while Fantastic Children could appeal more audiences. 

Both have a ton of plot holes that just keep surprising you. They have this similar "something bigger behind the scene" feeling to both of these stories and how they unfold. 

They both have very similar character designs and art styles, and have a similar directing style when it comes to drama.