It's more appropriate to compare him with Rooney. He's just not the same type of player as the other three, especially Scholes and Lampard.
Lots of people seem to be doing it, but for me it's horseshit. He's a midfielder. An attacking midfielder. He plays exactly as Lampard did. As Scholes did when he broke through.
His manager has harnessed his best attributes and told him to get in the ball as far forward as possible. But he's a midfielder. He has a responsibility to tackle and he creates a lot.
If you want to draw a Rooney comparison, feel free. You can even call Early Scholes, Lampard, Gerrard, and Alli '10's'. But Rooney was a center forward that dropped off. As Cantona or Sheringham did. The others are all midfielders that push on.
Irrespective of that, if people want to call him anything, they can. He's looking like he's going to be world class.