  We study the large $N$ $\theta$ dependence and the $\eta^\prime$ potential in
supersymmetric QCD with small soft SUSY-breaking terms. Known exact results in
SUSY QCD are found to reflect a variety of expectations from large $N$
perturbation theory, including the presence of branches and the behavior of
theories with matter (both with $N_f \ll N$ and $N_f \sim N$). However, there
are also striking departures from ordinary QCD and the conventional large $N$
description: instanton effects, when under control, are not exponentially
suppressed at large $N$, and branched structure in supersymmetric QCD is always
associated with approximate discrete symmetries. We suggest that these
differences motivate further study of large $N$ QCD on the lattice.
