If you want a great DD, go for the TT. If you want to experience what a pure sports car is suppose to be like, go for the GT3!

My choice would be the GT3. You can't go wrong with either choice, good luck!

 

Couple of other considerations, I went thru the same decision tree last yr and finally ordered a TT.
Keep in mind they are both street cars, if you're just planning a weekend toy either will do. For a pure track car the 3 is a better choice, as long as you can afford to wad up a 100k car at a DE, remember few, if any ,insurance companies are covering DE's at all anymore, puts a serious dampner on the track for me. You might be better off buying a cheaper dedicated track car that you don't mind writing off if you have to.
The fact is the TT is faster than the GT3 around the 'ring, leather seats and all. The TT is a ton more versatile as a DD as well. The backseats are a deal breaker for me. I have kids and they like to ride around with me on the weekend, so for me the 'weekend car' is a pipedream. Lastly, there's nothing wrong with a little comfort from time to time either.
If you're planning a DD at all, get the TT.

 

Daily driver? TT
3rd car / weekends? GT3
For an occasional track visit both would fit the bill nicely.
But as a few have mentioned, theres simply no wrong choice, both are fantastic.