Different JTAG debug options for ATmega1281
No answers; here's what I discovered:


Of these three, only the JTAGICE-mkII is supported by AVR Studio 4.  It's also old, expensive, and (relatively) slow.
The JTAGICE3 is the de-facto standard for a lesser-expensive Atmel JTAG programmer/debugger, and is supported in AS5 and AS6.
The ATMEL-ICE is brand new, represents Atmel's attempt to hit the lower-cost market, and is supposedly better than the JTAGICE3 in every way (speed, breakpoints, etc).  However, it hasn't gone through it's "new product growing pains" yet...


I chose to get the JTAGICE3, and migrate to Atmel Studio 6.  The migration was easy.  It took a while to figure out how to make the debugging work with AS6, but now it's working fine.