Huge difference between the two.
With Multiscreen, you end up with several different sets of files. There is one page that is launched, it sniffs the environment and directs to one specific set of output files. So, perhaps you have 300 topics. You might end up with say, 410 different files for each of the different outputs created. RoboHelp 2015 Release seems to include three layouts in the default configuration. So that would be a grand total of roughly 1,230 files to distribute.
Responsive is simpler. The same project in Responsive output would exist in a single set of files. Again, assuming 300 topics, you might end up with a total of 468 files to distribute. The coding causes the content to simply "adapt" to the available screen space.
Another bonus with Responsive output is that a nice interface is provided to customize it. Customizing Multiscreen is something not for the faint of heart. It's arcane to say the least.
Hopefully this helps... Rick 