I think that you lose some features with the SAM3X8E but I can't find a good comparison chart right now.
Atmel just released asf 3.5 and I got a sd card/Fatfs api working on a SAM3X-EK so that is exciting.
My goal is to get a standalone json/cgi server running, I think that can lead to some really cool "Internet of Things" applications.
What is the priority: Due Mini vs Due Net? Due Net would seem to be a little easier hardware wise but integrating FatFs/lwIP/SD card drivers might be a pain.
Regards