Sora no Otoshimono, Asobi ni Iku yo! Recommendations
Both have female "aliens" with incredibly advanced technology, abilities and weapons, who meet a guy in Earth. Also, the guy (and his friends) get involucrated with a dangerous organization (like Synapse in Sora no Otoshimono).
Both animes have a female alien coming from out of outer space witch stays with the main protagonist. They also both have amazing technology.
both have a strange alien girl who visits earth and meets the main protag.
in sora. its angels and in asobi. its cats
also both guys have a childhood friend that likes them