OK, found it
\hardware\arduino\sam\system\CMSIS\Device\ATMEL\sam3xa\include\sam3x8e.h
Gives you the base addresses of the peripherals on the SAM3X8E, and
\hardware\arduino\sam\system\CMSIS\Device\ATMEL\sam3xa\include\instance*
Holds a stack of .H files (one for each peripheral) with all the defines for the register addresses.
So at first glance it seems that the way the SAM is done is different to the LPC implementation.
LPC_UART0->THR
on an LPC would be
REG_USART0_THR
on the Due. Kind of makes you wonder what the point of CMSIS is, not much of an abstraction layer for the peripherals but maybe OK for the ARM core itself.
Where are all the beta testers, they should be experts by now and be able to describe this.
Rob