Responsive all the way - Adobe's not putting any effort into adding new stuff to Multiscreen, plus with that layout you have to package up multiple copies of your help to accommodate different screen sizes. HTML5 does that auto-magically ;>)
Indeed, as Jeff indicated all the new fun stuff is only being made available via the Responsive.
To expound on and clarify Jeff's statement about the differences, with Responsive output, you have a single set of output files. Perhaps you have 300 topics and maybe 450 output files. In Responsive, you only have to deal with that single set of 450 output files. But in Multiscreen, you have 450 output files for EACH of the different layouts. So if perhaps you have four layouts for Multiscreen, you end up with 1,800 different files to distribute or copy to the server.