fwiw I tend to favour a pecorino (fiore) sardo.
Pecorino is italian for "Sheep's milk cheese".
There is hundreds variety of Pecorino cheeses based on aging, technique, region of production and so on.
Pecorino Toscano is one of them, Fiore Sardo is another great variety.
Pecorino Romano is the most known Pecorino cheese and very often in the USA when someone says Pecorino they are referring to Pecorino Romano.
P Romano itself has several different varieties, white label, black label, genuine and so on, mostly based on aging and geographical provenience (Rome or Sardinia)
No matter what and with very few exception, Pecorino Romano is aged over 6 months and is usually very salted.
Pecorino Romano for ages has been used as a CHEAP alternative to Parmigiano Reggiano and Grana Padana.
I don't like neither Romano nor Reggiano on my margherita, but in essence a good quality place uses Parmigiano Reggiano, a cheap establishment thinks to be saving on food cost using Pecorino Romano.