  We compare a suite of four simulated dwarf galaxies formed in 10$^{10}
M_{\odot}$ haloes of collisionless Cold Dark Matter (CDM) with galaxies
simulated in the same haloes with an identical galaxy formation model but a
non-zero cross-section for dark matter self-interactions. These cosmological
zoom-in simulations are part of the Feedback In Realistic Environments (FIRE)
project and utilize the FIRE-2 model for hydrodynamics and galaxy formation
physics. We find the stellar masses of the galaxies formed in Self-Interacting
Dark Matter (SIDM) with $\sigma/m= 1\, cm^2/g$ are very similar to those in CDM
(spanning $M_{\star} \approx 10^{5.7 - 7.0} M_{\odot}$) and all runs lie on a
similar stellar mass -- size relation. The logarithmic dark matter density
slope ($\alpha=d\log \rho / d\log r$) in the central $250-500$ pc remains
steeper than $\alpha= -0.8$ for the CDM-Hydro simulations with stellar mass
$M_{\star} \sim 10^{6.6} M_{\odot}$ and core-like in the most massive galaxy.
In contrast, every SIDM hydrodynamic simulation yields a flatter profile, with
$\alpha >-0.4$. Moreover, the central density profiles predicted in SIDM runs
without baryons are similar to the SIDM runs that include FIRE-2 baryonic
physics. Thus, SIDM appears to be much more robust to the inclusion of
(potentially uncertain) baryonic physics than CDM on this mass scale,
suggesting SIDM will be easier to falsify than CDM using low-mass galaxies. Our
FIRE simulations predict that galaxies less massive than $M_{\star} < 3 \times
10^6 M_{\odot}$ provide potentially ideal targets for discriminating models,
with SIDM producing substantial cores in such tiny galaxies and CDM producing
cusps.
