Durarara!!, Psycho-Pass Recommendations
I'm surprised this hasn't been recommended yet. Both are alluring and dark, taking the average person into a world of chaos, crime and justice. Both appeal to a mature audience and dabble with a bit of the supernatural. Psycho Pass is set in a far futuristic version of Tokyo while Durarara is present day. Amazing seiyuu Kana Hanazawa and Miyuki Sawashiro play female leads in both. Psycho Pass' main focus is crime and police while Durarara is gang violence and the not so ordinary lives of three teenagers.
There are obvious similarities between Makishima and Izaya, and also some similarities between their respective nemeses – Kougami and Shizuo. Both are set in Toukyou, often in the dark. There's a certain focus on philosophy in each, which usually comes from Makishima or Izaya, but occasionally comes from other characters.
Watching Durarara!! reminded me a lot of Psycho-Pass with things like murder, and cops. Although Psycho-Pass isn't as of the supernatural type like Durarara!!, it still reminded me alot of eachother and I could make connections between them both.
Like Durarara!!, Psycho-Pass is a more serious-natured series set in a futuristic setting where humans are implementing a type of governing system in the attempts to create a peaceful, city society. However, there will always be those who do not agree with "City standards", as well as those with secrets and/or alterior motives - as both titles well portray.
On a side note, the main protagonist in both Durarara!! and Psycho-Pass is a young woman.