There are infinite advantages to the DSG if your sole goal is to go fast, the MT is archaic and slow. The DSG's only downside is the MT's only upside when talking about a car that is more for the track than anything else and that's weight and maintenance. If you are going to be tracking on a budget the MT is the way to go, one less thing to need expensive regular maintenance and a high cost if it detonates. As you can note from my sig, I went MT for my eventual race car but my "must go fast" car is a DSG, and would be even if they had offered it in MT.
If you are thinking Miata you would be amiss if you didn't consider the same exact car with a bit more personality. The Fiat 124 Abarth. As Hamster put it.......if you want the best Miata there is, get the Fiat 124 Abarth. An Italian car, built by the Japanese, it's got everything.
https://www.fiatusa.com/spider.html