The Flory-Huggins interaction parameter χ quantifies the excess free energy of mixing unlike species and governs phase behavior in polymer blends and block copolymers. Chain architecture affects how chains pack and interact in the melt, which can significantly influence χ. To explore this, we investigate χ for blends with different architectures of flexible bead-spring chains. We examine blends in which both chain species have a "polypropylene"bead-spring structure, but one species has beads with a slightly weaker interaction: Either the side beads (case 1), main chain beads (case 2), or branch point beads (case 3). We use molecular dynamics simulations and thermodynamic integration during "morphing"of one species to another to find χ for all three cases, for which random mixing models would give identical results. We find the strongest repulsion in the case of side beads, reflecting its higher accessibility to other beads. These systems provide an appealing test for PRISM predictions of structure and miscibility in polymer blends. We supply input to PRISM from simulations without any adjustment, and PRISM predictions are compared directly with simulation results. We find PRISM predictions for χ obtained using the Percus-Yevick (PY) closure (available in public PRISM modules but problematic in that it incorrectly predicts the dependence of χ on molecular weight) are inconsistent even in their signs and sensitive to the initial guess needed to solve the integral equations.