We have performed molecular dynamics simulations of blends composed of chemically realistic (CR) and lower barrier (LB) 1,4-polybutadiene (PBD) over a wide range of composition and temperature. In these blends, the dynamically fast component (LB-PBD, T-g approximate to 108 K) and dynamically slow component (CR-PBD, T-g approximate to 164 K) are conformationally, structurally, and thermodynamically very similar, with different dihedral barriers leading to significantly different segmental dynamics. We observe primary (beta-relaxation) and secondary main-chain (beta-relaxation) processes in the dielectric response of pure melts and CR-PBD/LB-PBD blends for all temperatures and compositions investigated. The separation between the dielectric alpha-and beta-relaxation processes of the fast component polymer significantly increases upon blending. This increasing separation dramatically influences the frequency-dependent dielectric susceptibility of the blend due to the significant strength of the fast component beta-relaxation process and the insensitivity of this relaxation process to the blend composition, providing a plausible explanation for the broadening of the blend dielectric response observed experimentally in a number of miscible blends. The results obtained from our simulations are discussed in light of concentration fluctuation, Lodge-McLeish, and coupling models.