  The standard cosmological paradigm currently lacks a detailed account of
physics in the dark sector, the dark matter and energy that dominate cosmic
evolution. In this paper, we consider the distinguishing factors between three
alternative models - warm dark matter, quintessence and coupled dark
matter-energy - and \lcdm{} through numerical simulations of cosmological
structure formation. Key halo statistics - halo spin/velocity alignment between
large-scale structure and neighboring haloes, halo formation time and migration
- were compared across cosmologies within the redshift range
0$\leq$$z$$\leq$2.98. We found the alignment of halo motion and spin to
large-scale structures and neighbouring haloes to be similar in all cosmologies
for a range of redshifts. The search was extended to low density regions,
avoiding non-linear disturbances of halo spins, yet very similar alignment
trends were found between cosmologies which are difficult to characterize and
use as a probe of cosmology. We found haloes in quintessence cosmologies form
earlier than their \lcdm{} counterparts. Relating this to the fact that such
haloes originate in high density regions, such findings could hold clues to
distinguishing factors for the quintessence cosmology from the standard model.
Although in general, halo statistics are not an accurate probe of the dark
sector physics.
