In this paper the results of simulations of axial and planar channeling of electrons and positrons in straight and periodically bent Si crystals are presented. Simulations with direct calculation of trajectories of projectiles accounting for all-atom interactions were carried out using the MBN Explorer software package. The full atomistic approach for particle trajectories simulation allows to quantitatively compare axial and planar channeling processes. The results of the simulations show significantly lower dechanneling length and number of channeling projectiles in the axial channeling case. For this case the dependence of characteristics of the channeling process on the choice of an axis direction and on a direction of the crystal bending have been investigated.