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We analyze joint angular distributions of a charmonium decay to the Ξ;Ξ̅ pair using the Ξ→Λπ→pπ-π weak decay chain for the cascade and the charge conjugated mode for the anticascade. The decays allow a direct comparison of the baryon and antibaryon decay properties and a sensitive test of CP symmetry in the strange baryon sector. We show that all involved decay parameters can be determined separately in vector and (pseudo)scalar charmonia decays into ΞΞ̅ due to the spin correlations between the weak decay chains. Contrary to the recently measured e+e-→J/ψ→ΛΛ̅ process, the transverse polarization of the cascade is not needed and has almost no impact on the uncertainties of the decay parameters. [ABSTRACT FROM AUTHOR]