None.
Great handling, surprisingly fast, sounds great. Looks fantastic. Bose Stereo sounds great even with top off on highway. Better gas mileage than my V-6 truck. I love this car, the way it feels, handles, and looks. I will baby this for as long as I own it, which will hopefully be for a long time.
Nice well made, good looking car, but better handling than a Boxster? You are aware it's only Golf components under the skin, right?
The TT's handling is average at best, and a Boxster would take it apart on any road or circuit you care to mention.
Audi TT is a car with worst handling ever. The first time that car was test-driven by a reporter (car magazine), was disaster (handling-wise)
The only thing Audi did, to solve this problem, was a plastic body kit and rear spoiler.
The car still corners like a damn truck, trust me, I used to own one.
Not sure what TT you've been driving, but the one I've got in the UK chews Boxsters up for fun on winding roads. The quattro is sweet, and although the obviously larger Porsche engine has the edge on the straights, it cannot live with the TT on country roads, which let's face it, most roads are not perfectly straight, and if they are they are pretty boring to drive along.
I can go in a straight line in a Datsun Cherry, but would I want to?
No. TT for me every time, and I own a 911 also, but the TT is so much more fun, and gets more admiring looks.