as I see it, the UX is related to how user interacts with your product in general.
The goal should be to provide a seamless UX regardless of the device, the connection and the user agent.
Having said that it is necessary to reckon with the skills and opportunities we have available to build and maintain the product.
RWD is something that needs a serious investment in the design phase and even more serious invesitment during the developing and Maintenance phases.
Before deciding which way to go we should answer some questions:
-Do we design according Mobile First approach?
-How we design the solution based on RWD?
-Do we rely on a specific framework (for example bootstrap)?
-If you follow that logic of this framework?
-How much you customize the logic of the framework (for example by adding and / or removing a breakpoint)?
-What would it cost us to do everything "house made"?