Davids and Emerson are intrinsically different players even though they more or less played the same position.
Davids was an attacking player no matter what position he played in (DM, LM, CM) because of his qualities and instincts as a player. Technically he is better than any DM I've seen, his dribbling and passing was probably good enough for an attacking midfielder and his work rate in getting back the ball could be attributed to his hunger to have it at his feet so he could attack himself, as opposed to passing it to the forwards/wingers.
His shooting was overrated as far as I'm concerned.The power was there alright but his shooting technique was the biggest problem; if he did connect well chances are it would bulge the net but that rarely happened most of the time.Emerson doesn't differ very much in that aspect.
However where it concerns having to stay back and cover for the defence full time as the first line of resistance Emerson holds the edge over Davids because of his discipline.While Edgar was usually all over the place and defending and attacking at the same time he could often be found missing when the team lost the ball and had to defend a counterattack.
Emerson had Dacourt to do the job he's doing for Vieira at the moment when he was at Roma, so we got to see him attack at every opportunity available and he did well as a third wave into the box or in hassling the opponents further up the field while Olivier stayed back.This season he's shown that he can fill the other role of staying back equally well and Vieira is having no qualms about storming forward and making his presence felt.To make a fairer comparison we'd have to place Edgar in the above two situations to find out but for what it's worth I think he's better in the former and worse in the latter, albeit only marginally.
Really makes me wonder what it'd be like having both him and Emerson in the team.