  We investigate the isotropic and anisotropic components of the Stochastic
Gravitational Wave Background (SGWB) originated from unresolved merging compact
binaries in galaxies. We base our analysis on an empirical approach to galactic
astrophysics that allows to follow the evolution of individual systems. We then
characterize the energy density of the SGWB as a tracer of the total matter
density, in order to compute the angular power spectrum of anisotropies with
the Cosmic Linear Anisotropy Solving System (CLASS) public code in full
generality. We obtain predictions for the isotropic energy density and for the
angular power spectrum of the SGWB anisotropies, and study the prospect for
their observations with advanced Laser Interferometer Gravitational-Wave and
Virgo Observatories and with the Einstein Telescope. We identify the
contributions coming from different type of sources (binary black holes, binary
neutron stars and black hole-neutron star) and from different redshifts. We
examine in detail the spectral shape of the energy density for all types of
sources, comparing the results for the two detectors. We find that the power
spectrum of the SGWB anisotropies behaves like a power law on large angular
scales and drops at small scales: we explain this behaviour in terms of the
redshift distribution of sources that contribute most to the signal, and of the
sensitivities of the two detectors. Finally, we simulate a high resolution full
sky map of the SGWB starting from the power spectra obtained with CLASS and
including Poisson statistics and clustering properties.
