Cold case is a drama with a female as the investigator of cold cases( cases that have gone unsolved). In Cold case the lead is also a female and they are basically solving the same kinds of murders or incidents. Cold case has more of a frigid vibe to it while mikaiketsu has a bright vibe because of its lead Haru.
The Investigation in Cold Case is more direct on crime stories. The Specialist drama, it also involved with crime stories, but both have different approaches on investigating. It is not like pure Sherlock and Detective investigation technique. It is more evolve in thinking patterns in a creative and logical path.