I would only use Display Channel as an editor tool, i.e. a way to preview how the page will look like in another device/screen size.

You can certainly use display channels to deliver a mobile-specific view of your Episerver site however it's far from being a replacement for responsive build techniques. Fundamentally, they are two different things. Responsive principles are about creating an experience which works regardless of device or screen size, and adaptive mechanisms such as display channels are about delivering different user experiences based on criteria such as user agent.

The route you should choose depends on the site and how users interact with it across different devices however it's extremely rare nowadays to find a situation where the responsive route isn't the best option. Also bear in mind that, even if you do want to tailor content for mobile devices, you could use personalisation while still retaining the benefits of a responsive site.

As an aside, display channels are not restricted to simply delivering mobile/non-mobile views - they can deliver differing views based on any criteria you care to write and so there are loads of use cases for this feature.

One final thing to consider if you do end up writing separate mobile views using display channels - You'll need to maintain a list of mobile user agents in order to deliver the right views for the device accessing the site.

Well put Paul. Also, keep in mind that you can add just resolutions (IDisplayResolution) to give editors a nice way to preview the content in different resolutions. You can see how this is done in the Alloy templates. These cannot be used as an adaptive mechanism to change what's renderd in the view, these will only change the screen size.

I am also working as a technical trainer and when I hold developer cources I always say to the students that they as Johan and Paul are saying can use display channels to help/guide the editors on how the page can/will look like in another device, but I also tell them that it is never an replacement on doing proper responsive design.

Thanks Folks! 

No confusion now :)