Both take place in future.
The same idea, that people with 'anomalies' work for organization against people having the same kind of 'anomalies'.
The same mood.
Both main characters are something like garbage.
Similar vibe, color scheme, and detective/hitman tones in both
If you enjoyed the sci-fi and crime aspects of Darker than Black, Psycho-Pass is a great show following that similar mix of topics.
Both of these animes are set in a Japan different than the one that exists today, and both heavily involve characters who are investigators, Psycho-Pass more so than Darker Than Black. The fast paced crime solving and back and forth between the "good" guys and "bad" guys (quotes because the audience is eventually led through a deconstructive lens) are factors of both of these shows that remind me of (and are just as good as) Deathnote. If you find that your heart misses the characters the most, you'll be able to find similar characters in Psycho-Pass and Darker than Black.
Both are based upon detectives trying to think like the enemy with mysterious occurrences.
Both series happend in the future, yet in Psycho Pass the society is more advanced than in DTB. Both series have male protagonists that are fighting themselves and against the society because their ideals are in conflict. In this series the evaluation of the good and bad concepts is recurrent, and this situation makes the characters struggle between what they want and what is consider the best to do.
Both have similar themes and a similar feel. Kirihara and Tsunemori have a lot in common, and Hei and Kogami are practically the same character, to say nothing of the similarities between Huang and Masaoka. My point is, though they are on different sides of the law, the main casts of both shows are similar, the shady organizations they work for have the same secretive, questionable feel. Moreover, both series have very well done villains and no one is evil for the sake of being evil.
These two anime both have systems that in some way segregate two sets of people. These anime aren't about a hero bringing one of these classes to glory, rather the separate classes just create a reason for why our heroes are doing what they do as jobs. As such, you get to see a story related to our heroes that ultimately has meaning more-so to them, not their society.
Darker than Black is more supernatural while Psycho-Pass is on the futuristic side so, the imagination definitely gets to play while watching either. Psycho-Pass however, has a more straight-forward plot.
Both psycho pass and darker than black are set in a similar futuristic world, with the police working to fight members of society with supernatural powers
It's mostly the mood; very dark, very bleak worlds where people who work on the fringes have to deal with daily moral ambiguities. You keep watching both of them for similar reasons. You wan to find out about the pasts of the characters, as well as your questions about who is good and who is bad in the story. In that way they also have similar themes so I think you would likely enjoy them in the same way even though the premises are somewhat different.
its is a very dark, action filled anime with the main male protagonists not displaying a lot of emotion.