One of them is located just behind the FTDI adapter chip and is labeled ICSP
The Due does not have an FTDI chip, it uses an Atmega16u2. The first header you refer to is a programming header for this Mega should you even need to reflash it.
The other is located immediate adjacent to the SAM3X chip next to the infinity symbol and Arduino Due logo silk-screened onto the top side of the board.
This is the actual SPI header and AFAIK the only access you have to the SPI port and therefore this is the header used by the SPI libraries.
Rob