That's not really true, is a huge difference between using Sodium vs Lead vs light water vs heavy water vs gas for the primary coolant loop.

http://en.wikipedia.org/wiki/Heavy_water_reactor

http://en.wikipedia.org/wiki/Light_water_reactor

http://en.wikipedia.org/wiki/Liquid_metal_cooled_reactor

http://en.wikipedia.org/wiki/Lead-cooled_fast_reactor

http://en.wikipedia.org/wiki/Gas-cooled_reactor

The real link has a lot more to due with how cheap uranium was to mine / refine and how much refined uranium was needed for weapons programs. At this point we could stop all uranium mining for the next 50+ years without any problems and by changing designs that could stretch out to something like 1000 years. Fuel is simply not the problem.