The nice thing about SharePoint’s device channels is that you don’t have to decide between them and responsive web design. You could certainly use both techniques on your site, but you would have to manage them slightly different since device channels are configured in the SharePoint site settings and RWD uses media queries in CSS3 style sheets. If you wanted to use device channels by themselves without RWD for mobile UI, here are some things to consider:
Device channels could require more assets to manage – If you are using device channels to swap out the entire master page, you would need to manage two or more master pages. Master pages can be complicated, unless you have a specific need, it would be better to use Device Channel Panels to just change parts of the UI rather than the whole master page.
Device channels rely on user agent strings – This is great if you can target your devices specifically from their user agent strings but can at times be limiting. For instance there are many varieties of Android devices from cellphones to tablets and many times their user agent does not declare the screen size. In some cases media queries can be more useful for targeting browser features like this.
Device channels require the publishing feature in SharePoint – This is a feature that is only available in the full SharePoint Server 2013 product, not SharePoint Foundation. Also, many SharePoint administrators prefer to only provide site owners with simple team sites; in these cases you wouldn’t have access to use device channels