To even consider this an "either or" is shortsighted nonsense; there is NOTHING that precludes one from the other, since if you've done your designing right with a semi-fluid and elastic layout, adding responsiveness shouldn't even break 2k at the end of your existing stylesheet -- ooh, not 2k1!!! :/
Honestly the two can work hand-in-hand since it's easier to make a fast lean site responsive than it is a fat bloated train-wreck of how not to build a website in the first place.
... which is a significant part of why I say that 99.99% of the people who call themselves "designers" because they can draw pretty pictures in Photoshop are giant tools who don't know enough about web technologies to be designing a blasted thing for anyone -- and that the approach of drawing a bunch of goofy pictures in Photoshop before you have logical document structure marked up semantically with a working CSS layout is putting the cart before the horse...
Of course, when people start out with hundreds of K of JS and CSS before they even start putting content into the document thanks to idiotic halfwit framework nonsense like bootcrap, such concepts are completely alien; hence my common recommendation that people go find a stick to scrape that off their boot before proceeding.