As the title states, this is something I been using a lot more and more just for the sake of the UX. A great example in this battle is the tab widget. Tabs are great on desktop computers but suits very badly in phone when you have content that are pretty large and long.
My solution to this is having a tab widget for my desktop and, if suitable, for the tablet, and then I make an accordion out of divs to display the same content on mobile instead of the tabs.
How does this affect the ranking on Google? There is obviously duplicate content, but how much will that penalize?