I think Detective Conan is best in the Japanese manga detective mystery genre. I am defining the detective mystery genre as including 1) character(s) which are formally or informally detectives and 2) crime or other malfeasance that takes place under mysterious/non-straightforward circumstance that the detective(s) uncovers the truth behind using investigation and logic. I think the biggest competitors for the title of best Japanese Detective Mystery are the Kindaichi series, Detective Academy Q, and Q.E.D. (Disclaimer: I haven't read all of the Det.myst. series out there, like Gosick) There are a few others that might also technically qualify like Ouroboros, Demonic Detective Nougami Neuro, and the manga adaptation of Higurashi When They Cry but I think they are lacking the key element of detective mystery genre excellence: Fairplay mysteries -- mysteries that are reliably and consistently solvable by readers of they pay attention and puzzle it out.
So out of the ones I mentioned above, I still think Detective Conan beats them out. Kindaichi is the weakest in my opinion with the flat characters being the number one problem, but it is also hurt by relatively low mystery variety, lack of a greater arc, and the mystery presentation style which involves way more panel hunting. Q.E.D. is a step up, similar to but better than Kindaichi. It also has much more variety. Detective Academy Q is my second favorite to DC, but I only know as far it has been translated. I like that there are a variety of detectives on a team, mysteries types, a greater arc. Conan does characters and mysteries better though and has better pacing within cases.