Do digital purchases from the old 3DS models carry over?
I think they've made that possible. But it's probably Nintendo-y and convoluted, not just signing in and re-downloading stuff.
I did the transfer process last year from a crappy used 3DS XL to a nicer new one, and it was pretty much painless. They have an option right in the settings to transfer everything right over, and then you either move your SD card from the old to the new or you transfer all the files to the new 3DS's SD card on your PC. It's pretty simple actually, surprisingly so.