  We study the rates and direct CP violations of two-body baryonic $\bar
B_{u,d,s}\to {{\rm\bf B}\overline{\rm\bf B}}'$ and $B^-_c\to{{\rm\bf
B}\overline{\rm\bf B}}'$ decays, where the final state baryons include
low-lying octet and decuplet baryons. We incorporate topological amplitude
formalism and the factorization approach. Asymptotic relations at large $m_b$
are used to simplify decay amplitudes. Using the most up-to-date data on $\bar
B^0\to p\bar p$ and $B^-\to\Lambda\bar p$ decay rates as inputs, rates and
direct CP violations of $\bar B_{u,d,s}\to {{\rm\bf B}\overline{\rm\bf B}}'$
decays are revised and predicted. It is interesting that the results on rates
satisfy all existing experimental bounds and some are close to the bounds.
Factorization diagrams contribute to penguin-exchange, exchange, annihilation
and penguin-annihilation amplitudes. Although the resulting penguin-exchange
factorization amplitudes are sizable, the rest suffer from severe chiral
suppression and are sensitive to non-factorizable contributions. The $\bar
B_s\to p\bar p$ decay rate predicted in factorization calculation is very rare,
but it can be enhanced by including non-factorizable contributions. The case
where the rate is enhanced to saturate the present experimental bound is
discussed. As annihilation modes $B^-_c\to{{\rm\bf B}\overline{\rm\bf B}}'$
decays from factorization calculation are found to be very rare, but they can
be enhanced by including non-factorizable contributions as well. Small direct
CP violations of pure penguin modes in $\Delta S=-1$ $\bar B_{u,d,s}\to{{\rm\bf
B}\overline{\rm\bf B}}'$ decays are robust predictions of the SM, while
vanishing direct CP violations of exchange modes in $\bar B_{u,d,s}\to{{\rm\bf
B}\overline{\rm\bf B}}'$ decays and in all $B^-_c\to{{\rm\bf B}\overline{\rm\bf
B}}'$ decay modes are null tests of the SM.
