My money is still on Newton as the greatest recorded brain.
I would go with Leonardo, John Stuart Mill (who I disagree with on most things), Newton, Thomas Paine, Thomas Jefferson and Benjamin Franklin.
I'd give Da Vinci the edge over Newton. There's no doubt that Newton was an absolute genius at mathematics, and this gave him some fundamental insights into the mathematical relationships of physics, but -- and I in no way mean this in disrespect -- mathematical geniuses are a dime a dozen, even if most of them never achieve any public recognition.
Da Vinci, however, was an innovater and world-class master of so *many* diverse fields, each one of them a career in themselves, each one of which would have insured his lasting fame if that one field was the only one in which he had made his accomplishments.
Painting, sculpting, architecture, anatomy, engineering, mechanics, optics, hydraulics, drafting, warfare, mathematics... He even made discoveries in meteorology, geology, and paleontology.
Newton was was one of the all-time greats in mathematics. Da vinci was one of the all-time greats in *everything* he put his mind to, including pursuits which are generally considered different "kinds" of genius -- how often do we expect brilliant artists to be scientific geniuses as well, or vice versa?
Still, the case could be made that Newton achieved more in mathematics than Da Vinci did in any one of his many fields of study, but the kind of versatile genius which can master everything it contemplates gets my vote over the kind which excels, no matter how superbly, in a narrower discipline.