  The hard X-ray sky at energies above 10 keV, has been extensively explored by
the Swift and the NuSTAR missions in the 14-195 keV and the 3-24 keV bands
respectively. The major population of the hard X-ray detected sources are AGN.
We compare the number count distributions derived from the swift 105-month
catalogue with those from the serendipitous NuSTAR source catalogue.
  In the 14-195 keV band, the Swift/BAT counts follow a Euclidean slope with
alpha=1.51+/-0.10 (90% confidence level).
  The NuSTAR counts in the 8-24 keV band present a steeper slope with alpha =
1.71+/- 0.2$, because of an upturn at fluxes below ~2x10^{-13} erg/cm2/s.
  The same upturn is observed in the soft (3-8 keV) NuSTAR number counts, which
in overall also present a steep slope with alpha = 1.82+/- 0.15.
  Only the bright part of the NuSTAR 3-8 keV counts agrees with the chandra
number counts in the 2-10 keV band while the fainter part (<7x10^{-13}
erg/cm2/s ) of the soft NuSTAR counts is in marked disagreement with the
chandra counts.
  Next, we compare the derived number counts in the different bands using our
X-ray AGN population synthesis models.
  The comparison between the Chandra and the Swift/BAT number counts shows a
very good agreement for the 'standard' AGN spectrum with a power-law slope
Gamma=1.9, a high energy cut-off at ~130 keV and a 2-10 keV reflection
component of 3%.
  On the other hand, using the above standard AGN spectral model, only the
bright part of the NuSTAR 8-24 keV and 3-8 keV number counts, agree with the
model predictions.
  Then it is most likely that the disagreement between the X-ray number counts
in the different bands is because of the faint NuSTAR number counts. We discuss
various possibilities for the origin of this disagreement.
