Hard X-ray surveys have proven remarkably efficient in detecting intermediate polars and asynchronous polars, two of the rarest type of cataclysmic variable (CV). Here we present a global study of hard X-ray selected intermediate polars and asynchronous polars, focusing particularly on the link between hard X-ray properties and spin/orbital periods. To this end, we first construct a new sample of these objects by cross-correlating candidate sources detected in INTEGRAL/IBIS observations against catalogues of known CVs. We find 23 cataclysmic variable matches, and also present an additional 9 (of which 3 are definite) likely magnetic cataclysmic variables (mCVs) identified by others through optical follow-ups of IBIS detections. We also include in our analysis hard X-ray observations from Swift/BAT and SUZAKU/HXD in order to make our study more complete. We find that most hard X-ray detected mCVs have P_{spin}/P_{orb}<0.1 above the period gap. In this respect we also point out the very low number of detected systems in any band between P_{spin}/P_{orb}=0.3 and P_{spin}/P_{orb}=1 and the apparent peak of the P_{spin}/P_{orb} distribution at about 0.1. The observational features of the P_{spin} - P_{orb} plane are discussed in the context of mCV evolution scenarios. We also present for the first time evidence for correlations between hard X-ray spectral hardness and P_{spin}, P_{orb} and P_{spin}/P_{orb}. An attempt to explain the observed correlations is made in the context of mCV evolution and accretion footprint geometries on the white dwarf surface. Comment: 14 pages, 8 figures and 3 tables. Accepted for publication in MNRAS