Ridge wave guide transitions have been used in the high power couplers of many ongoing high intensity Proton accelerator projects world wide. Because of their smaller size and high energy densities, they Require strict dimensional tolerances during fabrication and operating conditions. In order to study their Electro magnetic characteristics, two different types of transitions with a straight ridge and a tapered ridge are compared using full wave simulations. A part from the return loss and resonant frequency variation with dimensions, comparative studies on the phase shift, insertion losses, electric and magnetic field distributions and multipacting are also reported. This analysis will be useful in selecting the appropriate ridge wave guide transition for the RF couplers of accelerator cavities.