Texhnolyze, Wolf's Rain Recommendations
Similar atmosphere of dying world and hopelessness. They both are dark and sad seinens.
Similar atmosphere. Both have a female main character, who has special abilities. Both have have many male characters that are fighting (more or less) for a female main character.
Both stories tell us about survival in a post-apocalyptic world. Similar animation style and dystopian atmosphere. Both are serious and gloomy. Also, lead characters wander a lot.
both animes have slow moments allowing you to think about what is really going on
also both have same concept and similar atmosphere