We study the baryonic charmonium decays of B mesons B+→ηcK+ and B+→J/ψK+, where the ηc and J/ψ subsequently decay into a pp̄ or ΛΛ̄ pair. We measure the J/ψ→pp̄ and ΛΛ̄ anisotropy parameters αB=-0.60±0. 13±0.14 (pp̄), -0.44±0.51±0.31 (ΛΛ̄ ) and compare to results from e+e-→J/ψ formation experiments. We also report the first observation of ηc→ΛΛ̄. The measured branching fraction is B(ηc→ΛΛ̄)=(0.87-0.21+0. 24(stat)-0.14+0.09(syst)±0.27(PDG))×10-3. This study is based on a 357fb-1 data sample recorded on the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider.