  Our paper aims at providing an answer to the question whether one can
reliably describe the properties of the most important spin-isospin nuclear
excitations, by using the available non-relativistic Skyrme energy functionals.
Our method, which has been introduced in a previous publication devoted to the
Isobaric Analog states, is the self-consistent Quasiparticle Random Phase
Approximation (QRPA). The inclusion of pairing is instrumental for describing a
number of experimentally measured spherical systems which are characterized by
open shells. We discuss the effect of isoscalar and isovector pairing
correlations. Based on the results for the Gamow-Teller resonance in $^{90}$Zr,
in $^{208}$Pb and in few Sn isotopes, we draw definite conclusions on the
performance of different Skyrme parametrizations, and we suggest improvements
for future fits. We also use the spin-dipole resonance as a benchmark of our
statements.
