But me, I've always seen Sherlock Holmes more as a Superman guy.
Batman is a billionaire who wants to punish criminals, seeking vengeance for the death of his parents against all of crime. Young men love Batman movies because he's super-rich so he has all the hot cars and tech, plus he knows all kinds of kung fu and can beat up just about anybody . . . he's the teenage dream a male Katy Perry would have sung about, if male pop stars sang about boy things.
Superman, however, is a country boy who came to the big city to search for truth, both as a reporter and a superhero, and help people who are in trouble gain justice. When there is no one else to help you in Metropolis, there is always Superman, with powers and abilities far beyond those of normal folk.
Now, which of those sounds even remotely like Sherlock Holmes?
Too often, Batman is just not used as a detective. If you think of Gotham City as a house, he's the big, mean dog inside that scares some crooks away just by being there at night, and bites those who dare make their presence known. His main weapon is fear, his main skill is brutality, and, oh, yes, he's filthy, filthy rich and has a bat-Lamborghini and a bat-yacht and a bat-pool-boy.
Superman, however, exists in the daytime world, popularized by a writer he has a relationship with. He helps people with both the big, nation-threatening issues and the small cat-stuck-in-a-tree problems. He's not about gadgets or tricks, just using what powers he has when the need arises. His Moriarty is a big-thinker and an empire builder, not a scary chaotic madman. (Though Superman's Reichenbach did come from ending the threat of someone who matched his powers better . . . sorry, Lex.)
While Batman has long been seen as the greatest detective in comic books, and Sherlock Holmes the greatest detective in fiction, their core values are very, very different. Later writers have tried to give Sherlock Holmes a childhood trauma as a reason for his career choice, but it never sticks. Sherlock Holmes is a man whose powers emerged when he was younger and he saw fit to use them to help people. His brother, from the same "planet," has similar powers but put them to a different use. (Trying to make Mycroft the Supergirl of this metaphor doesn't entirely work -- Sherlock needs a young female cousin who also became a detective.)
It's early in the morning and a couple of my points in this argument have already slipped from my not-yet-warmed-up mind, but I think I'll be sticking with this "Sherlock Holmes is more like Superman" thesis, and they'll come back to me . . . which is good, because I have a feeling there are some Bat-fans out there who might disagree.
And if we are talking the more traditional fan use of the terms "Batlock" versus "Superlock?"
Oh, Superlock. Definitely Superlock.