Yondemasu yo, Azazel-san.

Same type of humor sometimes, but I think people that enjoyed Prison School will enjoy this as well. 

The cutest devils/spirits help out two clueless Misses in their daily tasks. [Sakuma is a part-timer in a detective-exorcist's office and Nanami is a newly appointed land Goddess.] Kamisama is more of a romance, while Azazel is naughtier, yet both are definitely comedies introducing the cutest little devils ever. 

Both series have demon protagonists serving as detectives whilst assisted by humans 

Both quite silly, but in the end so damn funny. Detroit Metal City is a lot more offensive, but if you watched Yondemasu yo, Azazel-san without any crying about it being offensive thet you'll be fine with Detroit Metal City. 

I got the same vibe from both anime. The vibe where in their worlds, nobody gives a sh*t about you're opinion and at the end of the day, it's all about making your life miserable. ! The theme ! DEMONS. Also, the detective guy in this is pretty similar looking to Oga Tatsumi XD  

I feel like the comedy style in both these anime are extremely similar, what I called before, "offensive-comedy". Both anime are suited towards more.. elder audiences IMO 17+ I'd say. If you enjoyed one of these, I'm sure you'd enjoy the other. I know I did.