We study the baryonic charmonium decays of B mesons, B+ to etac K+ and B+ to J/psi K+, where the etac and J/psi subsequently decay into a p pbar or Lambda Lambdabar pair. We measure the J/psi to p pbar, Lambda Lambdabar anisotropy parameters, alpha_B = -0.60 +- 0.13 +-0.14 (p pbar), -0.44 +- 0.51 +- 0.31 (Lambda Lambdabar) and compare to results from e+e- to J/psi formation experiments. We also report the first observation of etac to Lambda Lambdabar. The measured branching fraction is B(etac to Lambda Lambdabar) = (0.87 +0.24 -0.21(stat) +0.09 -0.14(syst) +- 0.27 (PDG)) x 10^-3. This study is based on a 357 fb^-1 data sample recorded on the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider.