When people discuss great NY pizza, they usually are talking about places where you sit down at a table and order a whole pie. You get brick ovens, the thin crust, fresh sauce and cheese, and ususlly a basil leaf or two on each slice.
In the 1970's, when I lived on West 85th Street, I had some favorite "slice pizza" places; i.e. places where you walked up to the counter, ordered a slice, and the guy stuck it in an oven to heat it up. This is really an entirely different species of pizza: the crust is a little thicker, the whole pie is usually larger, the sauce and cheese not as "gourmet", and it has no basil leafs (leaves?).
I find slice pizza every bit as good as whole pizza, but I don't think it gets the recognition it deserves. Would love to know the best places for it.