Migrating from ATMega2560 to ARM based -- Teensy vs Due?
If compatability is what you are after I would say go for the Due. If good products are what you are after, go for the Teeensy. The Due, being a real Arduino, will have the best software support and forum community and thus the best chance of getting existing libraries to work with it. The Teensy, because the project really centers around one guy's brilliance, is highly dependant on that one person's time, and while he has done a stirling job with the Teeensy core, he is still only one guy and can only do so much. So it may be harder to get third party libraries working on it.

That said, the Due is not a nice board. The SAM3X chips are awful. Any chip that needs an erase button attached to it to get around the "possibility it won't be able to enter the bootloader" (which incidentally is hard coded in ROM and can NEVER be replaced or upgraded) is destined for the scrap heap IMHO.

There are of course other options as well. There are about a million and one ARM based Arduino-like boards out there with varying amounts of support, either from the chip manufacturer (such as the ST boards), or third party builders. Then of course there are other architectures that are in my biased opinion much better than the ARM ones - chips such as the MIPS based PIC32, used in the chipKIT family of boards. Those latter though don't yet have a port of the SdFat library yet, although it is something that is being actively worked on. There are even Sparc based boards out there that are worth a look.