Exhuming the body of Fischer pretty much illustrates the advantage of live chess. Turn based chess seems fair considering the alternative, not taking turns.
Different objectives for each so, it's a draw. It would seem to me there's a continuum...all leading to playing face to face against an opponent with a pulse (someone else's phrase). Turn based would most clearly be an opportunity for study.
Which do you prefer and why?
By the way, while we are on the subject, is it just me, or (assuming a similar rating) are people on Live Chess comparably more difficult to beat than those who play Turn Based chess?