SharePoint Server 2013 offers new, optimized viewing experiences across different mobile platforms including a new way for designers to design a site once, and then based on that design render it using different Style Sheets and Master Pages, multiple times.
Resources on Device Channels:
Device Channels look very promising for many users of SharePoint but with the need to create and maintain multiple interfaces for Device Channels to work well, and the fact that there are new mobile devices every month with different screen resolutions, Responsive Design still is the way to go as Eric Overfield points out in this blog posting:
Eric has done some phenomenal work to create a Codeplex solution for modifying a popular responsive design framework namely Twitter Bootstrap. The goal of this project is to provide popular grid and responsive frameworks converted to SharePoint 2010 and SharePoint 2013.