Aquilani and Pizarro are like Pirlo attacking midfielders, moved backwards to the role of deeplying playmakers. Players that pick up the ball from the defence and take it to the attackers. Trying to create gaps and holes, to make chances.
De Rossi is more what they call a 'metodista'. A defensive midfielder, not exactly with the vision of a playmaker, but someone who does play with his head up and can pick a pass out and brings structure into a team. A pretty common player in Serie A, but rare outside of it.
If De Rossi would let Pirlo do, what he lets Aquilani/Pizarro do, there would be little difference in De Rossi's role.