AgI and AgCl reduction potentials
The answer is hard-soft acid/base theory (or HSAB theory). Essentially, some Lewis acids and bases are hard and some are soft, with a few borderline cases.


  Hard acids and bases tend to have



Small atomic/ionic radius
Highly charges (or highly positive/negative oxidation state)
High electronegativity for bases and low electronegativity for acids
Low polarizability



  Soft acids and bases tend to have



Large atomic/ionic radius
Low or zero charge / oxidation state
Moderate electronegativity
High polarizability


According to HSAB theory, matches that are hard-hard and soft-soft form strong interactions, where hard-soft matches are weaker interactions.

$\ce{Ag+}$ is a soft Lewis acid. $\ce{Cl-}$ is a hard Lewis base, while $\ce{I-}$ is a soft Lewis base. Therefore, we would predict that $\ce{Ag+}$ and $\ce{I-}$ will have have a stronger attraction than than $\ce{Ag+}$ and $\ce{Cl-}$.

We can see this difference in attraction in the solubilities of $\ce{AgCl}$ and $\ce{AgI}$ in water. $\ce{AgCl}$ is much more soluble in water than $\ce{AgI}$ (realizing that both are nearly insoluble). See the solubility constant data:


$\ce{AgCl}\ \ \ k_{\text{sp}}=1.8\times 10^{-10}$
$\ce{AgI}\ \ \ \ \ \ k_{\text{sp}}=8.5\times 10^{-17}$