All-dielectric electromagnetic band gap (EBG) waveguides structures promise significant improvement of accelerating gradient of laser-driven acceleration with the potential to miniaturize the accelerator itself. In this work we study photonic crystal structures designed for acceleration of relativistic electrons. We explore the performance of the all-dielectric EBG accelerating structures thanks to full wave electromagnetic simulations of couplers and accelerating waveguides. The characteristic interaction impedance, accelerating gradient and all the key parameters that are typically used to characterize linear accelerators are evaluated and used to compare the properties of the accelerating mode field distribution in different geometries.