We experimentally investigate the role of size effects and boundary scattering on the thermal conductivity of silicon-germanium alloys. The thermal conductivities of a series of epitaxially grown thin films with varying thicknesses and compositions were measured with time-domain thermoreflectance. The resulting conductivities are found to be 3 to 5 times less than bulk values and vary strongly with film thickness. By examining these measured thermal conductivities in the context of a previously established model, it is shown that long wavelength phonons, known to be the dominant heat carriers in alloy films, are strongly scattered by the film boundaries, thereby inducing the observed reductions in heat transport. These results are then generalized to silicon-germanium systems of various thicknesses and compositions; we find that the thermal conductivities of superlattices are ultimately limited by finite size effects and sample size rather than periodicity or alloying. This demonstrates the strong influence of sample size in alloyed nanosystems. Therefore, if a comparison is to be made between the thermal conductivities of superlattices and alloys, the total sample thicknesses of each must be considered.