We present a systematic comparison of the lattice structures, electronic density of states, and band gaps of actinide dioxides, AnO2 (An=Th, Pa, U, Np, Pu, and Am) predicted by the Heyd-Scuseria-Ernzerhof screened hybrid density functional (HSE) with the self-consistent inclusion of spin-orbit coupling (SOC). The computed HSE lattice constants and band gaps of AnO2 are in consistently good agreement with the available experimental data across the series, and differ little from earlier HSE results without SOC. ThO2 is a simple band insulator (f 0), while PaO2, UO2, and NpO2 are predicted to be Mott insulators. The remainders (PuO2 and AmO2) show considerable O2p/An5f mixing and are classified as charge-transfer insulators. We also compare our results for UO2, NpO2, and PuO2 with the PBE+U, self interaction correction (SIC), and dynamic mean-field theory (DMFT) many-body approximations.