Shawarma is not a taco, nor is it Greek ... at least not explicitly. It's really more of a Lebanese thing, and it's just marinated chicken, where TONS of chicken breasts are marinated, placed on a spit very tightly, and roasted. You cut pieces off by slicing down so you cut "strips" off each breast. It's very good. They also do this with lamb meat, and it's called "Gyro" meat (pronounced "Year-Ro"). It's also VERY good.
The "taco" you had is called a Gyro because it was originally made with Pita bread as the shell, gyro meat, feta cheese, onion, tomato, lettuce and a greek/lebanese yogurt sauce. Gyros are VERY good, and of course they are now made with chicken shawarma as well.
My father's side of the family is lebanese, so I grew up with lebanese cooking. Most of it is VERY good. To this day, we still have a lot of lebanese dishes during Christmas, Thanksgiving and Easter ... as well as other times. Mediterranean food is very good across the board if you ask me.