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ABSTRACT We present a suite of FIRE-2 cosmological zoom-in simulations of isolated field dwarf galaxies, all with masses of $M_{\rm halo} \approx 10^{10}\, {\rm M}_{\odot }$ at z = 0, across a range of dark matter models. For the first time, we compare how both self-interacting dark matter (SIDM) and/or warm dark matter (WDM) models affect the assembly histories as well as the central density structure in fully hydrodynamical simulations of dwarfs. Dwarfs with smaller stellar half-mass radii (r1/2 < 500 pc) have lower σ⋆/Vmax ratios, reinforcing the idea that smaller dwarfs may reside in haloes that are more massive than is naively expected. The majority of dwarfs simulated with self-interactions actually experience contraction of their inner density profiles with the addition of baryons relative to the cores produced in dark-matter-only runs, though the simulated dwarfs are always less centrally dense than in ΛCDM. The V1/2–r1/2 relation across all simulations is generally consistent with observations of Local Field dwarfs, though compact objects such as Tucana provide a unique challenge. Overall, the inclusion of baryons substantially reduces any distinct signatures of dark matter physics in the observable properties of dwarf galaxies. Spatially resolved rotation curves in the central regions (<400 pc) of small dwarfs could provide a way to distinguish between CDM, WDM, and SIDM, however: at the masses probed in this simulation suite, cored density profiles in dwarfs with small r1/2 values can only originate from dark matter self-interactions.