Hmm, that was worded poorly apparently, it wasn't an either-or question, but a yes/no. But I'll accept that as a yes.
Personally I wouldn't want to own either to drive. As technical achievements, they are amazing and deserving of a lot of praise. But reviews have universally panned both as being rather lifeless when it comes to driving. They are so busy driving FOR you, that you never feel like you're part of the experience. Even Randy Pobst, a Professional circuit racer, said the McLaren was so good at doing everything for you that he would just chuck it into a turn and let the computers sort it out.
The reason why I asked the question is nail down how you perceive "performance" and what you may expect from a "performance" car. My definition is different from yours.
To me a "performance" car needs to handle well, be responsive to my inputs, and communicate back to me what it going on. Being quick around a track is important, but that's not all of the picture in my opinion. I want to be involved in the driving process. I want the car to feel like an extension of myself, not some thing I'm just controlling.
So when you ask me, "Owning both which do you think performs better?" I will answer the BRZ.
When I got my STI, I thought it was a very responsive car. After upgrading the suspension to the point it is now, I thought it was a fantasticly responsive car and very communicative. But when I got the BRZ, I realized there was an entire level above my STI in those respects. Now it feels dull and kinda unresponsive. It does what I ask it to, but not with the alacrity of the BRZ.
The BRZ is the better performing sportscar in my opinon.