We examine the counts-in-cells (CiC) probability distribution functions (PDFs) that describe dark matter halos in the Dark Energy Universe Simulations (DEUS). We describe the measurements between redshifts z = 0 to z = 4 on both linear and nonlinear scales. The best fits of the gravitational quasi-equilibrium distribution (GQED), the negative binomial distribution (NBD), the Poisson-Lognormal distribution (PLN), and the Poisson-Lognormal distribution with a bias parameter (PLNB) are compared to simulations. The fits agree reasonably consistently over a range of redshifts and scales. To distinguish quintessence (RPCDM) and phantom (wCDM) dark energy from Λ dark energy, we present a new method that compares the model parameters of the CiC PDFs. We find that the mean and variance of the halo CiC on 2-25h
-1 Mpc scales between redshifts 0.65 < z < 4 show significant percentage differences for different dark energy cosmologies. On 15-25 h
-1 Mpc scales, the g parameter in NBD, ω parameter in PLN, and b and C
b parameters in PLNB show larger percentage differences for different dark energy cosmologies than on smaller scales. On 2-6 h
-1 Mpc scales, the kurtosis and the b parameter in the GQED show larger percentage differences for different dark energy cosmologies than on larger scales. For cosmologies explored in the DEUS, the percentage differences between these statistics for the RPCDM and wCDM dark energy cosmologies relative to ΛCDM generally increases with redshift from a few percent to significantly larger percentages at z = 4. Applying our method to simulations and galaxy surveys can provide a useful way to distinguish among dark energy models and cosmologies in general.