Having now dyed a doll with both iDye and RIT I can confidently say I prefer iDye for most BJD applications.
The colors are less accurate, but deeper and richer than you'd think. I was not able to make blue actually come out blue, which seems to be a common problem based on my internet research.
I've never tried to get blue from RIT, but I know it can be done.
RIT dye is easier to work with. It's less temperamental, takes more dunks to get a deep rich color so you can more easily control the shade you're going to end up with, and while warm you can kind of blend the color together before the piece dries and the color sets.