The existence of the The Two Detectives and The Two Criminals arcs in YuuMori always makes me giddy.
Yes, yes, let's show that William is just as capable of ferreting out a perpetrator and bringing them to justice as the Great Detective is. Yes, yes, let's show that Sherlock is just as capable of digging up an abusive asshole and committing a Perfect Crime to murder him as William is.
And, in fact, The Two Detectives ends with William getting the upper hand on Sherlock and (via trickery) managing to catch the perpetrator where Sherlock stalled out. And in The Two Criminals, Sherlock murdered Milverton before William could even get around to pulling the trigger.
They are equals. They are the same. They are both equally capable of Detectiving. They are both Detectives. They were both equally capable of elegant, seamless murderer. They are both Criminals.