"You have me confused for someone else." That is the phrase that is most common to communicate this. However, of the two examples that you provided, "You have me mixed up with somebody else." is better. You could also say "You've got me mixed up with somebody else."

They both mean the same thing. The first one "You have...." is better grammatically, but people will say both of these interchangeably. You could also just say "You mixed me up with somebody else" and it would have the same meaning.

As Matt says, they both mean the same thing. To me, the second one sounds better with the extra word "mate" at the end. * You got me mixed up with somebody else, mate.