Ther are to debugging conectors in the Arduino Due schematic.
10-pin (referred as JTAG) -> JTAG & Serial Wire (SWJ)
4-pin (referred as DEBUG) -> Specification?
I referred to the 10-pin connector and use the Segger J-Link 9-pin Cortex-M Adapter.
The J-Link 9-pin Cortex-M Adapter allows JTAG, SWD and SWO connections between J-Link and Cortex-M based target hardware systems.
I don't know where the 9-pin format came from, is it created by Segger? It does not seem to be an ARM standard.
Personally I prefer to use a header with a polarised housing. The key pin does the same job, but I am not going around cutting pins off headers... Seems a bad idea to introduce an incompatible standard, for a marginal improvement.
That 4 pin header (DEBUG) is a serial wire debug protocol (SWD) connector. It is another simpler protocol that only needs the data and clock lines to talk via serial between the SAM3X8E and the debugger.
In reference to dealing with surface components on the Due, I would recommend to be very careful. It happened to me twice that a capacitors just pop up the board and where hard to find in my workbench floor :). Regards!