I recently watched Vision of EscaFlowne (series, not the film), and it went straight into my top five. Very highly recommended. Parallels with Evangelion in the way that one protagonist in effect gets to choose the fate of the world.
Now watching Beast Player Erin (Kemono no Souja Erin). In some respects it's basically a children's anime, but it deals with pretty serious ideas about man and animals. It's beautiful to watch, all pastels and watercolours. It starts really slow (it's based on the same books that an on-going manga series is based on, but the anime take seven episodes to reach a point that is part of the first chapter of the manga!), but that's because of gently meticulous world-building. After the trauma of episodes 6 and 7 (if you keep a dry eye, you're just plain hard-hearted) the pace picks up - but it's never fast moving even so. Still, the story, the characters, the telling, are all really engaging, and it's going to be only the second four-cour series that I'll have watched complete, the first being FMA (OK third, 'cos I watched both versions of FMA). If you've got the time, and a degree of patience, don't hesitate.