Not all Geniuses are the Same
It is clearly established in all media that Sherlock Holmes' moment-to-moment observational and deductive abilities are exceptional.
Madame Simza Heron: What do you see?
Sherlock Holmes: Everything. That is my curse.
These powers are also held by Sherlock's brother, Mycroft. They engage in a childish game of deductive one-upmanship here:
Mycroft: Good evening, Sherly. I see your boot maker is ill, dear brother.
Sherlock: As I detect that you've changed the brand of soap with which you shave
Mycroft: May I point out the chimney in the front room on Baker Street is to the need of a damn good sweeping out?
Sherlock: Are you aware that the Hackney Carriage by which you arrived had a damaged wheel?
Mycroft: Yes, the left. And it's plain to the meanest intelligence that you've
recently acquired a new bow for your violin.
Sherlock: Same bow, new strings.
But Sherlock and Moriarty never engage in such a duel of observational power; Moriarty instead exerts their rivalry through the metaphor of a chess game. Moriarty's genius is in manipulation and control - the 'spider's web'.
This difference in gifting is demonstrated by the way that Sherlock generally does his own fieldwork (delegating to Watson and Heron when necessary), often in disguise, while Moriarty exerts his will through his henchmen whenever possible.
So there is no reason to ascribe Sherlock's abilities of observation - his 'curse' - to Moriarty.
In addition, Moriarty is under considerable mental load from bringing his complex plans to fruition.
Sherlock: With an empire so enormous, even You ... must keep a record of it somewhere.
James Moriarty may not always be concentrating on his immediate environment, making him vulnerable to Sherlock's daring fieldwork in disguise.