In many service systems such as movie theaters, sports clubs, or hotels, different customer segments share physical space, and the presence of customers from different segments may affect the utility a customer receives from the service. We consider a setting where two competing facilities offer service to two distinct types of customers and study whether and when the firms can benefit from using differential pricing. The two firms do not explicitly decide whether to use uniform or differential pricing. Rather, we derive our findings by characterizing and comparing all equilibria that might arise when differential pricing is feasible. Our results suggest that if the network externalities are symmetric, that is, if the two customer segments feel equally about the presence of customers of the other segment, then the firms never benefit from price differentiation, unless the network externalities are negative and strong when compared to the travel/inconvenience cost that the customers incur when receiving service from their less preferred facility. Interestingly, we find that using differential pricing can even hurt firm profits, when it leads to fierce price competition between the two service providers.