We compare the axial sectioning capability of multifocal confocal and multifocal multiphoton microscopy in theory and in experiment, with particular emphasis on the background arising from the cross-talk between adjacent imaging channels. We demonstrate that a time-multiplexed non-linear excitation microscope exhibits significantly less background and therefore a superior axial resolution as compared to a multifocal single-photon confocal system. The background becomes irrelevant for thin (< 15 microm) and sparse fluorescent samples, in which case the confocal parallelized system exhibits similar or slightly better sectioning behaviour due to its shorter excitation wavelength. Theoretical and experimental axial responses of practically implemented microscopes are given.