Why is AgCl less soluble than AgNO3?

In the comment to my previous answer, you asked for a theoretical reason for the solubilities not considering energy data. Since I know from energy considerations that the issue is not the solvation of the anions, I can present a reason based on the strength of the ionic bond in the two compounds. This reference (as well as others) states the the boning in AgCl has unusually high covalent character which makes it a tighter bond. The Ag+ ion and the Cl− ion are close to the same size (with the silver ion being smaller), so they can approach each other quite closely. In silver nitrate, the NO−3 ion is larger and does not allow as close an approach as the chloride ion, so the bond is weaker, easier to break up, and the salt is more soluble.