I understand this is an old forum but I'm new to this and this is a match up that interest me the most! I am a bigger fan of Sherlock holmes and initially was on his side for this match up, but after some thought I started to actually lean towards batman. Here is why.
First in this purticular mystery, according to the book, Holmes had more resources than just a magnifying glass to solve this mystery. He was able to figure out everything about the murderer because he had a tape measure and watsons medical knowledge. Watson confirmed Holmes's theory that poison was used. Holmes of course suspected it was poison but would never commit to a theory until he has proof that it was correct thus adding time to the investigation if Watson wasn't there. Batman, I think, could confirm this by himself quicker than Holmes because Holmes does limit what he stores in his memory bank to what he feels is relative. Where batman tries to learn everything about everything. Also if batman showed up as batman and not as Bruce Wayne then I'm sure Holmes would view batman as a greater mystery then who the murder was. We must remember that Holmes is addicted to solving the hardest mystery's. when confronted with two separate mystery's he is more intrigued with the more complex mystery and usually can't focus on both at the same time if they arent related. Finally, though Holmes is a great hand to hand combatant, he rather catch the criminal in a trap where the criminal is in no position to fight. Where batman is more of a predator and will Persue the criminal almost instantly after identifying them. So I think even if Holmes would figure out who the murderer was he would tactically wait to apprehend him in the safest way possible which, in several cases, has proven to take a long time. I hate to say it but I think batman would win.
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