As a pretty die-hard Buffetthead, I think an important question is- if all things were equal only Buffett were starting out today rather than when he did, would he be able to achieve the same degree of success?
I don't think there's any debate that, no matter what era you put him in, he's going to be one of the greats, however, I think there might be some valid debate regarding the degree of his success if he (and his general methodology) were operating in different periods of history.
I think Warren Buffett is "Warren Buffett" because he was an epic genius who happened to be in the right place at the right time in history. Shift a few variables either way and he might not have been as successful; yeah, I'd bet the farm that he would still be 'hugely successful' by all reasonable measures, but perhaps not the total freak of nature that he has been.
This discussion pertains to the original question, as it makes it very hard to pick a "next Buffett" ; there's a very real chance that the window of opportunity to become a "Buffett" to begin with has already closed (based on a number of different reasons).