There are no good independent measurements of market share between the various distributions of desktop Linux, and that is leading to a continued back-and-forth between rivals.
In the latest installment, Fedora leader Max Spevack takes a shot at Ubuntu leader Mark Shuttleworth, who last year estimated Ubuntu's distribution at eight million users and, recently, re-estimated that down to about six million: http://www.crn.com/software/202404605