We've got the new shape TT with the 3.2 lump in it (pretty rare as they stopped making them fairly quickly) and a zed, so this is coming from experience of driving both a lot over time.
In terms of things like the interior, panels, aircon, steering wheel and all that jazz, TT wins hands down. Absolutely fab quality, all the knobs work very well and feel solid, aircon is fast and very comfortable, road noise is low in comparison. Note: the sound system in the Audi is tonnes better than the Bose in the zed (although I am pretty sure it is also made by Bose).
In most other aspects, I very much prefer the zed. The ride, speed, power and all that stuff puts a smile on your face that doesn't exist when you're driving a TT. At the same time it's rear-wheel drive and has the looks in comparison to what is predominantly front-wheel drive (the 4-wheel drive system hardly ever kicks in in reality) and looks like a TT.
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If you want a powerful car that is fun and exciting, the zed is for you. If you want something to go to the shops in, keeps its value, blahdiblah blah blah, keep the TT. Despite the power and engine being somewhat similar, the feel is completely different. The TT's engine is set in perpendicularly within the bay to predominantly drive the front wheels and the layout is almost a straight-six (very narrow angle) which feels very different to drive than a genuine V6 motor.