No, you go down a bishop, and remain up two pawns. Equal. Qd2 gives better position though, and lets you win quicker.
Aggressive Response to 4...Nf6 in the Scotch
Well shepi's post 1009 is irrelevant, because most of those moves are bad for white. Once you finish that it'd be nice, but Qd2 is probably better.
Blacks king is horrible, and if you want to say not castling is a disadvantage, then why is the KG still played?
Then why is the Parham unacceptable, but this is:
Yes, Qxd4 is a blunder, that is why shepi put it in his post, so he could make the parham look bad, Qd2 gives white an obvious advantage.
Actually, I put it in my post because gavinator suggested it.

Anyways, although Qxd4 leads to an even game, I believe Qd2 is better, then white attack black's exposed and weak kingside.