Abstract The Sturtian and Marinoan snowball Earth episodes initiated 720 and 650 million years ago, respectively, are among the most dramatic events in Earth's history. The ultimate causes of these events remain obscure, however, and there is still uncertainty about the critical levels of greenhouse gas concentrations at which the snowball transition occurs. Furthermore, earlier modelling results (with incomplete representations of important boundary conditions) provided conflicting indications for differences between the critical carbon dioxide concentrations for the Marinoan and the Sturtian, reporting either the earlier or the later epoch to be more susceptible to global glaciation. Both the absolute values of and possible differences between these glaciation thresholds have profound implications for scenarios of snowball initiations during the Neoproterozoic. Here, we present coupled climate simulations (using an ocean general circulation model with dynamic/thermodynamic sea ice coupled to a fast atmosphere) focusing on the differences between the Neoproterozoic glaciations. For the first time, our simulations use realistic boundary conditions in terms of changes in solar luminosity between the two epochs and the most recent continental reconstructions. In agreement with previous studies with models including ocean and sea-ice dynamics, we report low values for the critical carbon dioxide concentration during the Neoproterozoic. But in contrast to hints from earlier studies we find very similar values of 100–130 ppm for the snowball bifurcation point during the Sturtian and Marinoan. This highlights the importance of realistic boundary conditions for climate simulations of the Neoproterozoic glaciations.