Let us cite a few points as disclosed in the Sherlock Holmes books by Sir Arthur Conan Doyle.
Let us try to know our man here who is Mycroft Holmes.
He is first introduced to us in The Adventure of the Bruce-Partington Plans
In this story, we get introduced to Mycroft Holmes. Here is how Sherlock describes Mycroft to John Watson.
Mycroft draws four hundred and fifty pounds a year, remains a subordinate, has no ambitions of any kind, will receive neither honor nor title, but remains the most indispensable man in the country
He has the tidiest and most orderly brain, with the greatest capacity for storing facts, of any man living. The same great powers which I have turned to the detection of crime he has used for this particular business. The conclusions of every department are passed to him, and he is the central exchange, the clearing-house, which makes out the balance. All other men are specialists, but his specialism is omniscience.
Mycroft was a large man and was extremely averse to any kind of field work, or contact with other humans.
This is what John observes when he first meets Mycroft:
Heavily built and massive, there was a suggestion of uncouth physical inertia in the figure, but above this unwieldy frame there was perched a head so masterful in its brow, so alert in its steel-grey, deep-set eyes, so firm in its lips, and so subtle in its play of expression, that after the first glance one forgot the gross body and remembered only the dominant mind.
Sherlock asks him “Why don’t you solve it ? You can see as far as I”, to which Mycroft replies…
‘Why do you not solve it yourself, Mycroft? You can see as far as I.’
‘Possibly, Sherlock. But it is a question of getting details. Give me your details, and from an armchair I will return you an excellent expert opinion. But to run here and run there, to cross-question railway guards, and lie on my face with a lens to my eye – it is not my métier.
This passage tells us that Mycroft dislikes the work part, but is very keen on analyzing the results.
In the case of The Greek Interpreter, Sherlock admits that his Intelligence may be hereditary. John asks why, to which Sherlock replies…
‘Because my brother Mycroft possesses it in a larger degree than I do.’
Some further explanations:
‘You wonder,’ said my companion, ‘why it is that Mycroft does not use his powers for detective work. He is incapable of it.’
‘But I thought you said-!’
‘I said that he was my superior in observation and deduction.
If the art of the detective began and ended in reasoning from an arm-chair, my brother would be the greatest criminal agent that ever lived. But he has no ambition and no energy. He would 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. Again and again I have taken a problem to him and have received an explanation which has afterwards proved to be the correct one. And yet he was absolutely incapable of working out the practical points which must be gone into before a case could be laid before a judge or jury.’
So we indeed see that Sherlock himself considers Mycroft to be a far better logician than him, but it is proven that he lacks the onus and ambition to do anything to that effect.
Hell, this is a guy who was one of the founding members of the Diogenes club.
To the uninitiated, the Diogenes club is a queer club where members are not allowed to talk or interact with each other.
Talking is the most serious offense and is grounds for expulsion.
So, in conclusion, Mycroft Holmes is indeed the smarter among the two.