the biggest difficulty with double knitting in the round, for me, is tension.
my knits and purls are close.. but my purls are just the littlest bit looser (unless i think about it!)
when flat double knitting, no problem--each side gets purled..
but in the round, every round is K1, P1, and all those purls are always on one side.. (and if i don't think about what i am doing, all those purls are looser.. not much but enough that one side is slightly bigger than the other!
In some ways, (chart reading!) working double knitting in the round is easier.. (no edges also makes it easier!)