We present results from a simulation of SU(2) lattice gauge theory with N(f) = 4 flavors of Wilson fermion and non-zero quark chemical potential mu, using the same 12(3) x 24 lattice, bare gauge coupling, and pion mass in cut-off units as a previous study (S. Hands, S. Kim, J.I. Skullerud, Phys. Rev. D 81, 091502(R) (2010)) with N(f) = 2. The string tension for N(f) = 4 is found to be considerably smaller implying smoother gauge field configurations. Thermodynamic observables and order parameters for superfluidity and color deconfinement are studied, and comparisons drawn between the two theories. Results for quark density and pressure as functions of mu are qualitatively similar for N(f) = 2 and N(f) = 4; in both cases there is evidence for a phase in which baryonic matter is simultaneously degenerate and confined. Results for the stress-energy tensor, however, suggest that while N(f) = 2 has a regime where dilute matter is non-relativistic and weakly interacting, N(f) = 4 matter is relativistic and strongly interacting for all values of mu above onset.