Content-centric networking (CCN) is a new paradigm to better handle contents in the future Internet. Under the assumption that CCN networks will deploy a similar congestion control mechanism than in today's TCP/IP (i.e., AIMD), we can build an analytical model of the bandwidth sharing in CCN based on the "square-root formula of TCP'". With this model we compare CCN download performance to what users get today. We consider different factors such as the way CCN routers are deployed, the popularity of contents, or the capacity of links and observe that when AIMD is used in a CCN network less popular content throughput is massively penalized whilst the individual gain for popular content is negligible. Finally, the main advantage of using CCN is the decrease of load at the server side. Our observations advocate the necessity to clearly define the notion of fairness in CCN and to design a proper congestion control to avoid less popular contents to become hardly accessible in tomorrow's Internet.