If you had asked me 5 years ago if it were better to design for a mobile device or a PC I would have responded emphatically that you needed both in order to survive in the current environment.
Now, I think the question barely makes the radar. Do you even need a full site for a PC, at all?
I was watching Shark Tank the other night, and 3 of the 4 products were already being sold, rather successfully, via their online site and/or Amazon.
Once upon a time, people would sit with their laptops on their lap (like I used to circa 2010), looking up things on the internet while you watched TV. Now, you sit on your comfy couch, ignoring your significant other, buying things you don’t need on Amazon Prime on your phone, no laptop needed.
Responsive Design was the solution that evolved from the growing Apple Store and Devices competing with the Android Store and devices. It was expensive and difficult to build and develop native applications for Apple and getting them into the iTunes store was time consuming. Add to that creating a separate and distinct native application for Android. That left a non-native option that would appear optimized on both the ever expanding PC screen and the ever shrinking mobile screens. Though, even that became difficult as the screen sizes became so diverse that some designers simplified the screen sizes to three the PC, Tablet and Phone.
So where does that leave UX and Designers?
Truly understanding the needs of the site, site owners, and audience should determine the focus of how the site displays to its best ability. Current metrics should play a significant part in seeing how people are using it today and how it can be best enhanced to accommodate those users you have and those you want to attract.