Osmotic coefficients and counterion distribution functions of rodlike and flexible polyelectrolyte chains have been studied using molecular dynamics simulations of multichain systems with explicit counterions in salt-free solutions. Using the counterion density profile, we have verified different regimes in the phase diagram of rodlike and flexible chains predicted by the two-zone model of Deshkovski et al. The agreement between our simulation results and predictions of the two-zone model is reasonably good for weakly charged rodlike chains. However, for flexible chains our results for the distance dependence of the counterion density profile in different regions of the phase diagram are only in qualitative agreement with the predictions of the two-zone model. The osmotic coefficient changes nonmonotonically with polymer concentration, in agreement with predictions of the two-zone model. The osmotic coefficient decreases with increasing polymer concentration in dilute solutions of both rodlike and flexible polyelectrolytes. In semidilute solutions of flexible chains the osmotic coefficient is an increasing function of polymer concentration. We have found that position of the minimum in the osmotic coefficient is close to the overlap concentration.