What changed in the new Due?
The 'new' board with green soldermask and the lighter headers is made by arduino.org.  The old one was probably made by the same company, but prior to the split in the founders.

Right now there is arduino.cc (the original website) and arduino.org (the website set up by the company that split from Arduino).  There is a lot of different perspectives about who really owns Arduino and I won't attempt to weigh in here.

The changes in firmware are still unknown.  It's likely that they are simple strings or response changes so the boards can be differentiated in software.  The new IDE is in alpha, and is yet another attempt to differentiate between the two Arduino groups.  I haven't attempted to program either with either group's IDE, but if I do I'll update this answer with the results.

At least there's a way to visually identify the difference once received - wish they had given them different part numbers so Digikey wouldn't have sent me a mixture...