Based on analysis by the non-partisan Tax Policy Center, here are graphical representations of both plans showing who gets the tax breaks under the plans. This will be the longest post I have ever published.
(Charts from Derek Thompson's Blog at The Atlantic.)
Perry 20% Flat Tax - Average Tax Break Per annual Taxable Income Group:
Cain's 9-9-9 Plan effect on Tax Liability per Annual Taxable Income Group: