Arguable. Burton's London is drawn in cartoonish swooshes with visible anachronism.
The Holmes in those films fights villains with modern political messages and technology forty years ahead of their time.
His personality flaws have been reduced to quirky character notes rather than the deep flaws of the BBC's Sherlock, so we don't have to deal with their consequences.
(By contrast, the BBC fetishises his flaws as the tragic necessity of genius.)
So while Cumberbatch's Sherlock flounces around in a swooshy cape coat, Downey's is smooth and suave in his tightly tailored suits.
Then there's Elementary, which brings Sherlock into the contemporary age as a character, rather than simply transplanting his Edwardian character into the modern day.
He's facing his flaws as horrible things which are not connected to his genius but rather a hindrance to them, and he's overcoming them.
He's got a short, tight haircut, week-old stubble, and tailored modern clothing. He's a man who isn't just living in this century, he's a man of this century.
None of them wear the deerstalker, but their profiles show very clearly how the past is being brought up to the modern day: transplanted, translated, or transformed.
