  Nuclear level densities (NLDs) and $\gamma$-ray strength functions (GSFs) of
$^{120,124}$Sn have been extracted with the Oslo method from proton-$\gamma$
coincidences in the ($p,p^{\prime}\gamma)$ reaction. The functional forms of
the GSFs and NLDs have been further constrained with the Shape method by
studying primary $\gamma$-transitions to the ground and first excited
states.The NLDs demonstrate good agreement with the NLDs of $^{116,118,122}$Sn
isotopes measured previously. Moreover, the extracted partial NLD of 1$^{-}$
levels in $^{124}$Sn is shown to be in fair agreement with those deduced from
spectra of relativistic Coulomb excitation in forward-angle inelastic proton
scattering.
  The experimental NLDs have been applied to estimate the magnitude of the
Porter-Thomas (PT) fluctuations. Within the PT fluctuations, we conclude that
the GSFs for both isotopes can be considered to be independent of initial and
final excitation energies, in accordance with the generalized Brink-Axel
hypothesis. Particularly large fluctuations observed in the Shape-method GSFs
present a considerable contribution to the uncertainty of the method, and may
be one of the reasons for deviations from the Oslo-method strength at low
$\gamma$-ray energies and low values of the NLD (below
$\approx1\cdot10^{3}-2\cdot10^{3}$ MeV$^{-1}$).
