Holmes and Clay are alike in being geniuses. They are smarter than other men.
At least as important, their minds operate in different ways from other men. They think, to use a contemporary cliché, outside the box. They operate in the underworld realm of criminal activity which most Londoners don't know exist; they act to mislead others without explaining their actions. They are both motivated in part by pride.
As for the differences, there are a few, but almost all revolve around their ethics and their relative position in society. Holmes is a good guy, Clay a villain. Clay engages in crime, Holmes stops it. Clay weakens the social structure, Holmes strengthens it.