Different types of tunneling trajectories contribute to 2D vibrationally assisted tunneling in semiclassical approximation. Two families of periodic trajectories compete on the potential energy surface (PES) with two symmetrically situated saddle points. Depending on the temperature, either 1D or 2D periodic orbits give the major contribution to the rate constant K(T) for the incoherent transition. As a result, an additional crossover temperature T(c2) appears that corresponds to the bifurcation of the extremal tunneling trajectory. In the coherent case both periodic and aperiodic paths contribute to the spectroscopic splitting DELTA of degenerate vibrational levels, and competition between these trajectories occurs even on simple PES with the only saddle Point. Contribution from aperiodic paths depends upon the quantum number of the promoting vibration. Bifurcation diagram for the two-proton transfer in free-base porphyrin is constructed. Its analysis show that at PES parameters, chosen to fit the experimental rate constant, the transfer follows the asynchronous mechanism closely up to low temperatures. Tunneling splitting in cyclopentanone is evaluated. Dominating a periodic paths make the transition configuration of vibrationally excited cyclopentanone strongly bent, rather than planar. These paths become "switched of" at a small coupling strength between two coordinates.