  We present a new set of high-resolution hydrodynamic cosmological zoom-in
simulations that apply the Feedback In Realistic Environments (FIRE) physics to
both Local Group (LG)-like and isolated Milky Way (MW)-like volumes (ten host
systems in total with baryonic particle mass $\simeq 3,500-7,000\,M_\odot$). We
study the stellar mass functions, circular velocity or mass profiles, and
velocity dispersions of the dwarf galaxy populations. The simulations reproduce
the stellar mass function and central densities of MW satellite dwarfs for
$M_\ast \geq10^{5.5}\,M_\odot$ and predict the existence of $\sim3$
unidentified galaxies with $M_\ast\sim10^5\,M_\odot$ within $300$ kpc of the
MW. Overall, we find no evidence for the classical missing satellites or
too-big-to-fail (TBTF) problems for satellite galaxies in our sample. Among the
satellites, TBTF is resolved primarily by subhalo disruption and overall mass
loss; central density profiles of subhalos are of secondary importance. For
non-satellite galaxies, our LG-like simulations predict as many as $\sim10$
as-of-yet unseen galaxies at distances $0.3-1$ Mpc from both hosts, with
$M_\ast\simeq10^{5-6}\,M_\odot$ (in halos with $V_\mathrm{max}\sim
20~\mathrm{km\,s}^{-1}$), albeit with large halo-to-halo variance. None of our
simulations produces a compact, baryon-dominated, high-density dwarf
elliptical-type galaxy (with $V_\mathrm{circ} \gtrsim 35~\mathrm{km\,s}^{-1}$
at $r<1\,$kpc), of which six may appear in the LG (but none in the MW). It may
therefore remain a challenge to reproduce the full diversity of the dwarf
population, including both the highest and lowest density systems.
