  We study the decays of $J/\psi$ and $\psi(3686)$ to the final states
$\Sigma(1385)^{0}\bar\Sigma(1385)^{0}$ and $\Xi^0\bar\Xi^{0}$ based on a single
baryon tag method using data samples of $(1310.6 \pm 7.0) \times 10^{6}$
$J/\psi$ and $(447.9 \pm 2.9) \times 10^{6}$ $\psi(3686)$ events collected with
the BESIII detector at the BEPCII collider. The decays to
$\Sigma(1385)^{0}\bar\Sigma(1385)^{0}$ are observed for the first time. The
measured branching fractions of $J/\psi$ and
$\psi(3686)\rightarrow\Xi^0\bar\Xi^{0}$ are in good agreement with, and much
more precise, than the previously published results. The angular parameters for
these decays are also measured for the first time. The measured angular decay
parameter for $J/\psi\rightarrow\Sigma(1385)^{0}\bar\Sigma(1385)^{0}$, $\alpha
=-0.64 \pm 0.03 \pm 0.10$, is found to be negative, different to the other
decay processes in this measurement. In addition, the "12\% rule" and isospin
symmetry in the $J/\psi$ and $\psi(3686)\rightarrow\Xi\bar\Xi$ and
$\Sigma(1385)\bar{\Sigma}(1385)$ systems are tested.
