For round one, I'd have to say Brian Finch. I've watched and am a fan of both series (including the Limitless movie, and most of the Sherlock Holmes mediums) and I've deduced that, while Brian Finch is on NZT he's got nigh-omnicompetence, his brain cells literally changing their physiology at some stages to fit his needs. Sherlock, however, still falls susceptible to human faults.
This is evidenced in both the BBC series and the books that Sherlock is a man. A hyper-intelligent man, but a man nonetheless. He still has addictions, he still has sexual desire, and he still forgets things. He can't dig it up like that without proper time and concentration, something he can't whip up on the go. This is the idea Sir Arthur Conan Doyle tries to convey to his readers: Sherlock may seem like an unfeeling sociopath but he is just as human as the rest of us.
Brian Finch, however, is something else. While on NZT, that twelve-hour time period he is the smartest man on the planet, full stop. That drug is, well, a drug and can enhance cognitive senses and processes in the brain to the fullest extent, and in some parts, beyond. Sherlock feels pain: he got shot in the BBC series, and was writhing in agony. Rebecca, while on NZT, got shot as well and was able to physically block the pain nerves in the brain by thinking about it, effectively cutting off nerves so she couldn't feel the pain of a bullet going through her shoulder. Sherlock forgot a simple room number that he saw glancing by, because he has to 'delete something', while Eddie Morra on NZT can literally remember when he was inside his mother's womb, where the brain wasn't even fully developed yet.This proves that, while Sherlock still has a base human composition, NZT gives a physical advantage on a chemical level of biology, which helps for. Finch wins.
Round two, however, is much much different. Both get prep, and both are smart enough with prep to probably topple a government if they needed to. Brian Finch has his ridiculous intellect and while Holmes lacks just a miniscule amount in that department, he has a much wider range of resources. He has his brother, who pretty much runs the entire country, and with some persuasion can possibly get numerous assets that would run Finch to the ground. Finch, however, doesn't have that. He has a shitty FBI desk which won't do jack for him because it's America. However, Finch has an advantage on improvisation. I'd have to say inconclusive.
Gee, writing so much on two of my favourite franchises, what a surprise.