  We explore generic ground-state and low-energy statistical properties of
many-body bosonic and fermionic one- and two-body random ensembles (TBRE) in
the dense limit, and contrast them with Random Matrix Theory (RMT). Weak
differences in distribution tails can be attributed to the regularity or
chaoticity of the corresponding Hamiltonians rather than the particle
statistics. We finally show the universality of the distribution of the angular
momentum gap between the lowest energy levels in consecutive J-sectors for the
four models considered.
