Using $1310.6\times10^6$ $J/ψ$ and $447.9\times10^6$ $ψ(3686)$ events collected with the BESIII detector at the BEPCII $e^{+}e^{-}$ collider, the branching fractions and the angular distributions of $J/ψ$ and $ψ(3686)$ decays to $Λ\bar{\Lambda}$ and $Σ^0\bar{\Sigma}^0$ final states are measured. The branching fractions are in agreement with, and much more precise than, the averages of previously published results. The polar angular distributions of $ψ(3686)$ decays are measured for the first time, while those of $J/ψ$ decays are measured with much improved precision. In addition, the ratios of branching fractions $\frac{\mathcal{B}(ψ(3686)\toΛ\bar{\Lambda})}{\mathcal{B}(J/ψ\toΛ\bar{\Lambda})}$ and $\frac{\mathcal{B}(ψ(3686)\toΣ^0\bar{\Sigma}^0)}{\mathcal{B}(J/ψ\toΣ^0\bar{\Sigma}^0)}$ are determined to test the "12\% rule". ; Comment: 10 pages, 8 figures