iDOLM@STER Xenoglossia

loli on mecha. you dont really have to say more.  

Both are about girls that destroy meteorites that are heading to earth. 

Both are stories in which a teenager unexpectedly becomes a pilot of a mecha and has to fight to save the Earth, while also retaining some level of an everyday life. They also both have hints of a romantic subplot, which become more important as the series go on. Solving conflicts through communication is a common theme as well. An important thing to note is that Fafner is more action focused, while Xenoglossia is mostly focused on the everyday lives of the pilots, however there is a good amount of character focused drama in both. Heavy inspiration from Evangelion in both shows as well. 

They seem similar in that they have women politing the mechas. Rinne is more echi though 

Female Main Cast with a mix of action and slice of life/humor. Both offer a bitter taste of tragedy. To me Xenoglossia essentially feels like a better version of Mai-Hime.  

Both series have a plot where an ordinary girl trains to become a mecha pilot, all the while fighting off an unknown enemy. Both have common themes and there's even a Gunbuster parody in Xenoglossia. 

Similar in using robot to protect the world (whole story) 

Girls fighting of the forces of evil while still at school. Though not in massive mecha. 

Both have robots though iDOLM@STER has cuter characters. It's also about saving the world. Just a different story plot. Both animes are fun to watch. IDOLM@STER though is not as good as Evangelion imo. ^^