Both are mystery dramas and deal with special cases.Both have genius but weird lead characters and both dramas are awesome.
Both are dramas about locks. In both dramas the main lead is some sorta lock otaku. Though, that's pretty much the one and only similarity in these 2 dramas.
While MONSTERS is mainly focused on Comedy as opposed to the seriousness of the crimes themselves, both that and Kagi no Kakatta Heya are played out very similarly, have slightly aloof, out of the box characters as the main crime-solver and they're both focused on episodes that are sort of fixed (more so Kagi than MONSTERS) and can be watched whenever; watching them in order isn't really needed.
Both lean heavily in the the classical detective genre -- genius and eccentric main character with sidekicks, one case per epiosde, focused on solving the crime (or unlocking the room, in Kagi's case), not a lot of character development or other plot.
Kagi No Kakatta is less slapsticky and has less puns but there are also quite a lot of Japanese-comedy scenes.
Kagi No Kakatta is less slapsticky and has less puns but there are also quite a lot of Japanese-comedy scenes.
Both shows are about a brilliant mind - that isn't connected to the police - investigating crimes. However, whileas Kagi no Kakatta Heya dwells on locked room cases, Hard Nut! shows cases that were solved by the usage of mathematics. If you like the investigation genre, Kagi no Kakatta Heya is a sure pick for you anyway.