Raindrops in warm clouds grow faster than predicted by classical cloud models. One of the possible reasons for this discrepancy is the influence of cloud turbulence on the coagulation process. In Part I (Siewert et al., 2014) of this paper series, a turbulent collision kernel has been derived from wind tunnel experiments and direct numerical simulations (DNS). Here we use this new collision kernel to investigate the influence of turbulence on coagulation and rain formation using two models of different complexity: a one-dimensional model called RAINSHAFT (height as coordinate) with cloud microphysics treated by a spectral bin model (BIN) and a large-eddy simulation (LES) model with cloud microphysics treated by Lagrangian particles (a so called Lagrangian Cloud Model, LCM). Simulations are performed for the case of no turbulence and for two situations with moderate and with extremely strong turbulence. The idealized 0- and 1-dimensional runs show, that large drops grow faster in the case turbulence is taken into account in the cloud microphysics, as was also found by earlier investigations of other groups. For moderate turbulence intensity, the acceleration is only weak, while it is more significant for strong turbulence. From the model intercomparison it turns out, that the BIN model produced large drops much faster than the LCM, independent of turbulence intensity. The differences are larger than those due to a variation in turbulence intensities. The diverging rate of formation of large drops is due to the use of different growth models for the coagulation process, i.e. the quasi-stochastic model in the spectral BIN model and the continuous growth model in LCM. From the results of this model intercomparison it is concluded, that the coagulation process has to be improved in future versions of the LCM. The LES-LCM model was also applied to the simulation of a single 3-D cumulus cloud. It turned out, that the effect of turbulence on drop formation was even smaller as the turbulence within the cloud was weaker than prescribed in the idealized cases. In summary, the use of the new turbulent collision kernel derived in Part I does enhance rain formation under typical turbulence conditions found in natural clouds but the effect is not very striking. © 2015 The authors.