  We determine the anisotropy of the spin fluctuation induced pairing gap on
the Fermi surface of the FeAs based superconductors as function of the exchange
and Hund's coupling $J_{H}$. We find that for sufficiently large $J_{H}$,
nearly commensurate magnetic fluctuations yield a fully gapped
$s^{\pm}$-pairing state with small anisotropy of the gap amplitude on each
Fermi surface sheet, but significant variations of the gap amplitude for
different sheets of the Fermi surface. In particular, we obtain the large
variation of the gap amplitude on different Fermi surface sheets, as seen in
ARPES experiments. For smaller values of Hund's coupling incommensurate
magnetic fluctuations yield an $s^{\pm}$-pairing state with line nodes. Such a
state is also possible once the anisotropy of the material is reduced and three
dimensional effects come into play.
