How you navigate to avoid the hills is immaterial, provided you can.
Thats the difference right there. In an RNP departure you can navigate with enough track miles to outclimb terrain. On a VOR based departure you can't unless you make the specified height for the weight you are at because your only navigation options are to A) navigate visually or B) fly a straight line back to the VOR and there is a hill in the way from many points on the departure and even if you are above deer park when you cross the VOR you have to turn north and track a radial which requires a certain climb gradiant that you won't have unless you made good in the visual segment.