The interplanetary coronal mass ejections ( ICMEs) and the corotating interaction regions ( CIRs) are the two most important structures of the interplanetary medium affecting the Earth and the near-Earth space environment. We study the solar wind-magnetosphere coupling during the passage of ICMEs and CIRs, in the Solar Cycle 23 ( Jan. 1995-Dec. 2009), and their relative geoeffectiveness. We utilize the timings of different features of these structures, their arrival and duration. As geomagnetic parameter, we utilize high time resolution data of Dst and AE indices. In addition to these geomagnetic indices, we utilize the simultaneous and similar time resolution data of interplanetary plasma and field, namely, solar wind velocity, interplanetary magnetic field, its north-south component and dawn-dusk electric field. We apply the method of superposed epoch analysis. Utilizing the properties of various structures during the passage of ICMEs and CIRs, and variations observed in plasma and field parameters during their passage along with the simultaneous changes observed in geomagnetic parameters, we identify the interplanetary conditions, plasma/field parameters and their relative importance in solar wind-magnetosphere coupling. Geospace consequences of ICMEs and CIRs, and the implications of these results for solar wind-magnetosphere coupling are discussed.