An idealized simulation setup is developed motivated by laboratory experiments with the Pi Chamber and previous model simulations of the Pi Chamber dynamics and microphysics. Pi Chamber experiments consider interaction between turbulence, CCN activation, and cloud droplet growth in moist Rayleigh-Bénard convection driven by the temperature and moisture difference between homogeneous horizontal boundaries. The focus here is on comparison of simulations applying traditional Eulerian bin microphysics scheme with simulation using a novel particle-based Lagrangian approach to simulate CCN activation and droplet growth. The Eulerian bin microphysics solve the evolution equation for the spectral density function, whereas Lagrangian approach follows evolution in time and space of computational particles referred to as super-droplets. Each super-droplet represents a multiplicity of natural droplets that makes the Lagrangian approach computationally feasible. The two schemes apply identical representation of CCN activation and use the same droplet growth equation; these make the direct comparison between the two schemes practical. Steady-state droplet spectra averaged over the entire chamber are similar, with the mean droplet concentration, mean radius and spectral width close in Eulerian and Lagrangian simulations. The differences are explained by the inherent differences between the two schemes and their numerical implementation. However, as one might expect, the local droplet spectra differ substantially, again in agreement with the inherent limitations of the theoretical foundation behind each approach. Comparison between simulations, laboratory experiments, and previous theoretical studies of droplet growth in the turbulent environment will be discussed.