  By employing the variational approach, density matrix renormalization group
(DMRG), exact diagonalization as well as symmetry and mean-field analyses, the
ground state properties of the two-bath spin boson model with simultaneous
diagonal and off-diagonal coupling are systematically studied in the sub-Ohmic
regime. A novel quantum phase transition from a doubly degenerate "localized
phase" to the other doubly degenerate "delocalized phase" is uncovered. Via the
multi-D1 ansatz as the variational wave function, transition points are
determined accurately, consistent with the results from DMRG and exact
diagonalization. An effective spatial dimension $d_{eff} = 2.37(6)$ is then
estimated, which is found to be compatible with the mean-field prediction.
Furthermore, the quantum phase transition is inferred to be of first order for
the baths described by a continuous spectral density function. In the case of
single mode, however, the transition is softened.
