BBC's Sherlock portrays Sherlock Holmes and Mycroft Holmes as smart, but one might be smarter. The Holmes brothers inherited their genius from their mother, while their father is depicted as the "sane one," who isn't as superhuman as the rest of the family. While Benedict Cumberbatch's Sherlock has honed his skills for criminal investigation, Mark Gatiss' Mycroft is in the British government and involved with the British Secret Services, the CIA, and MI6.
Sherlock claims that his brother is smarter than him, although lazier. As kids, Mycroft thought Sherlock was an "idiot" until they met other children and realized they were both highly intelligent. But just because the brothers thought Sherlock was the lesser of the two when it came to brains, that doesn't mean it's necessarily true. Especially considering Sherlock is younger, so he would naturally take some time to grow into his intelligence as a kid.
Sherlock Is The Smarter Holmes Brother
Sherlock is the smartest of the Holmes brothers in BBC's Sherlock. He outsmarts and tricks Mycroft multiple times in the series, such as when he drugs Mycroft and steals his laptop in Sherlock season 3, episode 3, "His Last Vow." Mycroft is only able to sometimes get leverage on Sherlock, thanks to his government position. And if he really wanted to, Sherlock would probably be able to get a similar or more high-ranking job, gaining some power over his brother. But he doesn't trust the government—with good reason considering some of his brother's actions—and is more focused on small crimes.
Mycroft also has to hire Sherlock for several cases, including in season 1, episode 3, "The Great Game," and season 2, episode 1, "A Scandal in Belgravia." Mycroft has more resources than Sherlock, so if he is truly smarter, he could solve these cases himself. Sherlock claims Mycroft is lazier than him, but Mycroft shows plenty of initiative throughout Sherlock—usually when pursuing his brother. It's possible his position in government is holding him back, but he's still shown to break the rules when he wants and has free time to spy on Sherlock. Mycroft knows Sherlock has a superior intellect, and that's why he turns to him so much.
Mycroft Is Smarter In Conan Doyle Canon
Although Sherlock is smarter in BBC's Sherlock, Mycroft is the more intelligent Holmes in Arthur Conan Doyle's original Sherlock Holmes stories. That said, he's also actually much lazier than his brother. Sherlock describes Mycroft as specializing in "omniscience" for the British government, consulting on different matters and providing solutions without ever getting his hands dirty or putting in any effort. In the short story "The Adventure of the Greek Interpreter," Sherlock says, "Again and again I have taken a problem to [Mycroft], and have received an explanation which has afterwards proved to be the correct one."
But the canonical Mycroft "will not even go out of his way to verify his own solutions, and would rather be considered wrong than take the trouble to prove himself right." Mycroft rarely wavers from his routine, which involves visiting just three locations: his home, his job in Whitehall, and the Diogenes Club. This all presents a very different character from the one portrayed by Mark Gatiss, who frequently ventures into the world for work and to spy on Sherlock and who does seem to care about being right. While BBC Sherlock's Mycroft has to do labor sometimes, the canonical Mycroft gets by with his brains alone.
Sherlock & Mycroft Holmes Have Different Types Of Intelligence
Though the Holmes brothers seem to have similar kinds of intelligence in BBC's Sherlock, they're actually very different, which makes it hard to say one is definitively smarter than the other. Sherlock has more practical knowledge. Though he's not exactly street smart, he could survive on the streets better than Mycroft. And though he's cold and socially awkward, he's more capable of making friends than Mycroft, as shown by his relationships with John, Molly, Mrs. Hudson, and Lestrade—proving he has social intelligence that Mycroft lacks.
Mycroft's intelligence makes him more suited for the government. He's clever and can hold his own in the field, as shown when dealing with his sister Eurus in Sherlock season 4, episode 3, "The Final Problem." But he's not as smart about interacting with people, forming relationships, and investigating. Sherlock could do what Mycroft does, but Mycroft could never do what Sherlock does.