Serial Experiments Lain, Tenshi no Tamago Recommendations
Both give off a similar feel-- eerie, otherworldly, surreal, and at least to me it makes me feel calm. Little dialogue and lots of symbolism
Both deal with abstract concepts about the nature of humanity.
Both give the viewer a creepy feeling due to their slow pace and dark atmosphere. There is very little dialogue so it leaves their story open to interpretation, and many believe them to have religious undertones.
They are quite old and the art is similar, with rather realistic character designs and strange yet beautiful backgrounds at times.
However, Serial Experiments Lain is an anime where technology is almost omnipresent, while Tenshi no Tamago is a movie that takes place in a world that seems not to have any. But despite these differences, I think their mysterious side makes them really similar.
Similar artwork, both anime rely upon silence to generate suspense and gives a surreal and meaningful nature to the show. Both display different perspectives of humanity and question it in a thought provoking manner.