Wideband suppression of zero order and relevant strongly asymmetric transmission can be obtained in photonic crystal gratings that are made of linear isotropic materials and show the broken structural (axial) symmetry, even if zero diffraction order may be coupled to a Floquet-Bloch (FB) wave at the incidence and exit interfaces. The studied mechanism requires that the peculiar diffractions at the corrugated exit interface inspire strong energy transfer to higher orders, including those not coupled to an FB wave. At the opposite direction of incidence, transmission due to zero and some higher orders that may be coupled at the corrugated input interface can vanish. This leads to the alternative scenario of wideband unidirectional transmission, which itself does not need but can coexist with the other scenario based on the merging of asymmetric diffraction and dispersion of the FB mode.