We analyze the effect of net neutrality regulation in a two-sided market framework when content is heterogeneous in its sensitivity to delivery quality. We characterize the equilibrium in a neutral network constrained to offer the same quality vis-à-vis a nonneutral network where Internet service providers are allowed to engage in second-degree price discrimination with a menu of quality-price pairs. We find that the merit of net neutrality regulation depends crucially on content providers' business models. More generally, our analysis can be considered a contribution to the literature on second-degree price discrimination in two-sided platform markets. (JEL D42, D43, D85, L51, L86, L88)