  We compare spherically-averaged radial number counts of bright (> 10^5 Lsun)
dwarf satellite galaxies within 400 kpc of the Milky Way (MW) and M31 and find
that the MW satellites are much more centrally concentrated. Remarkably, the
two satellite systems are almost identical within the central 100 kpc, while
M31 satellites outnumber MW satellites by about a factor of four at deprojected
distances spanning 100 - 400 kpc. We compare the observed distributions to
those predicted for LCDM suhbalos using a suite of 44 high-resolution ~10^12
halo zoom simulations, 22 of which are in pairs like the MW and M31. We find
that the radial distribution of satellites around M31 is fairly typical of
those predicted for subhalos, while the Milky Way's distribution is more
centrally concentrated that any of our simulated LCDM halos. One possible
explanation is that our census is bright (> 10^5 Lsun) MW dwarf galaxies is
significantly incomplete beyond ~ 100 kpc of the Sun. If there were ~8 - 20
more bright dwarfs orbiting undetected at 100 - 400 kpc, then the Milky Way's
radial distribution would fall within the range expected from subhalo
distributions and alos look very much like the known M31 system. We use our
simulations to demonstrate that there is enough area left unexplored by the
Sloan Digital Sky Survey and its extensions that the discovery of ~10 new
bright dwarfs is not implausible given the expected range of angular anisotropy
of subhalos in the sky.
