What are the differences in overtones for hard vs soft materials?
I am not sure if this is exactly answering your question but it may help you in your modeling efforts.  The metallic strings are going to be fairly simple to model in that the differential equations you use will be only dependent on the shape of string at any given time and the tensile strength of the string.

The nylon strings exhibit non-linear viscoelastic behavior which has a time dependent component to it.  That means that is has a memory and the local velocity of the string will be important.  By memory I mean there is residual strain built in once plucked and the time for recovery will be much greater than the frequency of motion.  I believe this is what gives it a “softer” sound.  Classically viscoelastic materials are modeled with a spring and damper in parallel.  

Descretizing the string over a number of elements and using a divided differences approach to approximate the differential equations you should be able to get a theoretical sense of how these differences affect the observed signal.

Hope that is helpful for you in thinking about your problem.