Show content based on width?

As you said making a part responsive would be the best way you can choose.
Working with screen width is some thing client side, and that’s done by CSS or alternatively by Javascript.

If it’s related to css, media queries will do the job:
http://www.ibm.com/developerworks/library/wa-cssqueries/index.html

and if it’s js, width property of screen object does the trick:
http://www.w3schools.com/jsref/prop_screen_width.asp