Now there's no doubt that after the re-export job was done there were garage bands all across the States readapting the Stones to their own environment, and on that garage band front, given the sheer volume that's out there you'd probably go America, but there's another little point that raises an interesting alternative.
I've seen a couple of comments along the lines that if you were white and playing the blues Stateside authenticity was vitally important. I've remarked elsewhere that I passed on the first Paul Butterfield in favour of Cream because the Butterfield was too authentic. In an environment where your music is rated on how accurately it reproduces the original that's fine.
My overall impression of the British situation, on the other hand, was that bands got as close as they could to the original while acknowledging that they weren't going to get all the way there, and when they'd reached the limits of their technical abilities they headed off in other directions.
One move was towards rave up territory, which gave us, for example, the Yardbirds and, with a fair dash of whimsy thrown in, the early, Barrett-era Pink Floyd, and the other was towards the artier approach that gave us, for example, Waterloo Sunset and A Whiter Shade of Pale (to pick two random examples).
The same thing happened (more or less) with the thousands of garage bands that sprang up across North America, but there’s one difference that leans towards Britain, and that's the influence of English eccentricity that comes down through the Goons, Monty Python and, particularly, the Bonzo Dog Band.
I find it difficult if not impossible to envisage a personal musical universe that doesn't include Vivian Stanshall and the Bonzos.
In any case, looking to the past with a view to catching up on things you missed first run through, I'd definitely be going British, if for no other reason that the multitude of American garage bands means you'd be flat out figuring out where to start.
The other way of looking to the past is to go and revisit past glories. Now, at first I was inclined to go British again, based on the fact that once you've taken out the black influences the Beatles, the Stones, Cream and the various British prog rockers were major influences on what came next.