Which properties control the strength of strong interactions? Does the strong nuclear force depend on mass, charge or spin? Accordingly, can we order neutron-neutron, proton-proton and neutron-proton pairs by the strength of the strong force between them? 
 A: The picture is basically "upside-down" or rather "inside-out":
According to our most current understanding, mass, charge and spin for the particles you are asking about, are actually the by-product of the elementary constituents of the Proton,Neutron and other baryons/mesons. 
All particles mentioned are actually combinations of 3 quarks ( or $qqq$ those would be baryons),  and one quark plus one anti-quark (or $q\bar{q}$, those would be mesons).
Quarks are spin 1/2 elementary particles, which have very small masses (not enough to make up the composite particle's mass) and broken charge (-1/3,2/3).
the composites particle's characteristics are the results of the 3(2) quarks that compose them, charges add up, spin is the result of angular momentum addition, and mass is the result of the interaction energy, we perceive that energy as mass.
Again, as per our current understanding, the strong force is nothing but a "Van der Waals" type force for the basic color force.
Obviously all of this is a broad-stroke overview, and I suggest you look into QCD and "the eightfold way".   
Since (AFAIK) the strength of the color force is not affected by spin/mass/charge (they do not affect the QCD interaction term), I would have to answer no - these interactions should be similar to an amazing degree...
Even so, it might be beneficial to look into some tables of those interactions. I would look in the Particle Data Group tables (http://pdg.lbl.gov/), to see if indeed there is some asymmetry there.
