  (Shortened Abstract). We analyze a redshift sample of Abell/ACO clusters and
compare them with numerical simulations based on the truncated Zel'dovich
approximation (TZA), for a list of eleven dark matter (DM) models. For each
model we run several realizations, on which we estimate cosmic variance
effects. We analyse correlation statistics, the probability density function,
and supercluster properties from percolation analysis. As a general result, we
find that the distribution of galaxy clusters provides a constraint only on the
shape of the power spectrum, but not on its amplitude: a shape parameter 0.18 <
\Gamma < 0.25 and an effective spectral index at 20Mpc/h in the range
[-1.1,-0.9] are required by the Abell/ACO data. In order to obtain
complementary constraints on the spectrum amplitude, we consider the cluster
abundance as estimated using the Press--Schechter approach, whose reliability
is explicitly tested against N--body simulations. We conclude that, of the
cosmological models considered here, the only viable models are either Cold+Hot
DM ones with \Omega_\nu = [0.2-0.3], better if shared between two massive
neutrinos, and flat low-density CDM models with \Omega_0 = [0.3-0.5].
