Well, my understanding is that in general, the more processed the food (including meat), the worse it is for our health.

Gyro / shawarma meat is evidently heavily processed and then reconstituted in to the 'cone,' likely with a bunch of salt, binding agents and preservatives added. Not unlike sausages, for example.

So almost any type of meat that goes in to a shawarma / gyro, such as lamb, beef, chicken, etc is going to be considerably better for us when eaten straight-up, as with steaks, etc.