Well, Hargreaves and Essien were not defensive midfielders in the first place!

Essien played Lamp's role in his national team and Hargreaves is an attacking midfielder before he was converted to a defensive midfielder. Which means to say that both players can adapt and is flexible in playing at either attacking or defensive positions.
Also notice that both players are pacy? Pacy players have advantage in Soccer.

Whereas for players like Gattuso, Hamman, Deschamps and Dunga, their primary role is defensive midfielder. They were taught to play in that position and they sticked to it till now (or till retirement).
So i guess flexibility is the key.

Cheers.
CK