Batman once deduced a rainbow monster that shot colored beams of varying effects that attacked Gotham came from a volcano and could only be defeated in one, based on no information what so ever. Greatest. Detective. Ever.
For real you all know Sherlock runs this with skill, but hes cheating too. Although Batman may have computers, Holmes has his drug addiction. It does even out the playing field a bit considering hes not always going without his own...resources. in fact many times hes been made out to be somewhat reliant on the stuff. With that in mind, I say Bats for both.
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