After doing some sightseeing, Batman succeeds in taking down Moriarty Jr. thanks to some unexpected help.
"My eyes ... I've rolled them too far back!"
This actually seems like a pretty good match. They're both detectives, they're both rich, they both have sidekicks. We can picture Batman and Holmes sitting together at the country club, sipping champagne and being condescending to the Hispanic waiter. So what's the problem?
Math. Math is the problem. Holmes first showed up in 1887, and he was 33 at the time. This comic came out in the late 1980's and is completely set in the present ... meaning Holmes is roughly impossibly fucking old.
"If I put literally anything into my body my century-old system won't be able to handle it."