EDIT: this was in A Study in Scarlet
Also they by the second book, Arthur Conan Doyle dropped that entirely. His characterization really started from Sign Of Four (The second book). The first one, Study in Scarlet, presented Watson's characterization more than Holmes'.
Holmes was a modern man. If they were on their prime on the same times, Holmes would still be better because he could get the same results as Batman without the Millionare budget. The tools would change but the results would be the same. Just look at BBC Sherlock (not Elementary, Sherlock).
...And does Mr. Goddanm Batman says so much as ''Thanks''? OF COURSE not. That'd hardly be GRIM AND GRITTY, would it?
-DKU's Jim Gordon.
It's as was stated before, Holmes is technicaly the better deductive detective, but generally, it's because he could "max his sliders" at deducting real world stuff in them odern area as opposed to having to consider alien stuff as well. It would be very, very close, going by top feats for both.
At any rate, the 'best detective' argument is moot since Adrian Monk is better than either of them.