  We investigate the electronic structure of the 2H and 3R polytypes of
NbS$_2$. The Fermi surfaces measured by angle-resolved photoemission
spectroscopy show a remarkable difference in size, reflecting a significantly
increased band filling in 3R-Nb$_{1+x}$S$_2$ compared to 2H-NbS$_2$, which we
attribute to the presence of additional interstitial Nb which act as electron
donors. Thus we find that the stoichiometry, rather than the stacking
arrangement, is the most important factor in the difference in electronic and
physical properties of the two phases. Our high resolution data on the 2H phase
shows kinks in the spectral function that are fingerprints of the
electron-phonon coupling. However, the strength of the coupling is found to be
much larger for the the sections of bands with Nb 4$d_{x^2-y^2,xy}$ character
than for the Nb 4$d_{3z^2-r^2}$. Our results provide an experimental framework
for interpreting the two-gap superconductivity and "latent" charge density wave
in 2H-NbS$_2$.
