We have used an atomistic ab initio approach with no adjustable parameters to compute the lattice thermal conductivity of Si0.5Ge0.5 with a low concentration of embedded Si or Ge nanoparticles of diameters up to 4.4 nm. Through exact Green's function calculation of the nanoparticle scattering rates, we find that embedding Ge nanoparticles in Si0.5Ge0.5 provides 20% lower thermal conductivities than embedding Si nanoparticles. This contrasts with the Born approximation, which predicts an equal amount of reduction for the two cases, irrespective of the sign of the mass difference. Despite these differences, we find that the Born approximation still performs remarkably well, and it permits investigation of larger nanoparticle sizes, up to 60 nm, not feasible with the exact approach.