  The Milky Way's Galactic Center harbors a gamma-ray excess that is a
candidate signal of annihilating dark matter. Dwarf galaxies remain
predominantly dark in their expected commensurate emission. In this work we
quantify the degree of consistency between these two observations through a
joint likelihood analysis. In doing so we incorporate Milky Way dark matter
halo profile uncertainties, as well as an accounting of diffuse gamma-ray
emission uncertainties in dark matter annihilation models for the Galactic
Center Extended gamma-ray excess (GCE) detected by the Fermi Gamma-Ray Space
Telescope. The preferred range of annihilation rates and masses expands when
including these unknowns. Even so, using two recent determinations of the Milky
Way halo's local density leave the GCE preferred region of single-channel dark
matter annihilation models to be in strong tension with annihilation searches
in combined dwarf galaxy analyses. A third, higher Milky Way density
determination, alleviates this tension. Our joint likelihood analysis allows us
to quantify this inconsistency. We provide a set of tools for testing dark
matter annihilation models' consistency within this combined dataset. As an
example, we test a representative inverse Compton sourced self-interacting dark
matter model, which is consistent with both the GCE and dwarfs.
