Let $X$ be a smooth cubic threefold over $\mathbb{C}$. Let $F(X)$ denote the Fano variety of lines in $X$, which is a smooth surface of general type.

Is this class of surfaces distingushed amoungst surfaces of general type?

I appreciate that this question is slightly vague. What I am looking for is something like a geometrical characterisation of such surfaces, say in terms of certain geometric invariants (i.e. hodge numbers, chern classes,...?). If this is too naive to hope for, then perhaps they have distinguished moduli, for example by forming a connected component of the moduli of surfaces of general type.