Joe Blow appears to be correct in suggesting that "you must be joking" is more common today than "you must be kidding." But far more common (since 1980) than either "must be kidding" or "must be joking" in the Google Books library is "got to be kidding" (sometimes spelled "gotta be kidding").
Here is an Ngram graph of "must be joking" versus "must be kidding" versus "got to be kidding" versus "gotta be kidding" for the period from 1900 to 2007:
The phrase "got to be joking" (not included in the above Ngram graph), by the way, seems to be less common than any of the four phrases in this Ngram graph—between half and two-thirds as common as "must be kidding" and "gotta be kidding" in the period between 2000 and 2007.
Does "you've got to be kidding" mean anything different from "you must be joking"? I don't think so. To my ear, though the former sounds more informal than the latter, it expresses the same combination of disbelief and a (possibly friendly) challenge to the hearer to clarify the previous statement, expand upon it, or admit that it wasn't intended seriously.