With the advent of social media, different companies often promote competing products simultaneously for word-of-mouth diffusion and adoption by users in social networks. For such scenarios of competitive diffusion, prior studies show that the weaker product will soon become extinct (i.e., "winner takes all"). It is intriguing to observe that in practice, however, competing products, such as iPhone and Android phone, often coexist in the market. This discrepancy may result from many factors such as the phenomenon that a user in the real world may not spread its use of a product due to dissatisfaction of the product or privacy protection. In this paper, we incorporate users' privacy for spreading behavior into competitive diffusion of two products and develop a problem formulation for privacy-aware competitive diffusion. Then, we prove that privacy-preserving mechanisms can enable a "coexistence equilibrium" (i.e., two competing products coexist in the equilibrium) in competitive diffusion over social networks. In addition to the rigorous analysis, we also demonstrate our results with experiments over real network topologies.