A coaxial Bragg resonator can be performed in four kinds of structures: it is constructed by inserting a regular waveguide between two selective Bragg reflectors (being called the upstream reflector and downstream reflector, respectively), or it consists of only two Bragg reflectors without regular waveguide section between them, where connection of these two reflectors is smooth with phase difference Δ=0 or is step-changed with corrugation phase difference Δ = +π or −π, respectively. The present paper is devoted to a comparative study for the response of reflectivity and quality factor on frequency in these four kinds of coaxial Bragg resonators, including the influences of the location and corrugation-phase difference of the step-changed connection of the two reflectors. Results show that a coaxial Bragg resonator possesses most attractive properties when the corrugation-phase difference is Δ = +π at the point of connection and the upstream reflector is longer than the downstream reflector.