  In this paper, we present the hard X-ray spectral analysis of a complete
sample of AGN de- tected by INTEGRAL/IBIS. In conjunction with IBIS spectra, we
make use of Swift/BAT data, with the aim of cross-calibrating the two
instruments, studying source variability and con- straining some important
spectral parameters. We find that flux variability is present in at least 14%
of the sample, while spectral variability is found only in one object. There is
general good agreement between BAT and IBIS spectra, despite a systematic
mismatch of about 22% in normalisation. When fitted with a simple power-law
model, type 1 and type 2 sources appear to have very similar average photon
indices, suggesting that they are powered by the same mechanism. As expected,
we also find that a simple power-law does not always describe the data
sufficiently well, thus indicating a certain degree of spectral complexity,
which can be ascribed to features like a high energy cut-off and/or a
reflection component. Fixing the reflection to be 0, 1 or 2, we find that our
sample covers quite a large range in photon indices as well as cut-off
energies; however, the spread is due only to a small number of objects, while
the majority of the AGN lie within well defined boundaries of photon index
(1<{\Gamma}<2) and cut-off energy (30<Ecut<300 keV).
