A damage in a structure alters its dynamic characteristics; namely, natural frequencies, modal damping values, and mode shapes. Changes also occur in some of the structural parameters such as: the mass, damping and stiffness matrices of the structure. Among different algorithms developed for structural damage identification, changes in either mode shape curvature or uniform load surface (ULS) curvature, derived from measured modal properties, have shown promise for locating structural damage. However, to date there is not a study reported in the technical literature that directly compares these two promising methods. The numerical results in this paper attempt to fill this void in the study of damage detection methods. In this paper, a numerical study is investigated to compare the robustness of these two methods in damage detection using the frequencies and mode shapes of the first few modes. Also, the application of a damage localization algorithm to these two methods in detecting and locating damage is demonstrated. The numerical results show that both of the two methods can accurately locate single damage with different damage characteristics (location and severity). However, the two methods have shown less sensitivity to specific types of damage when applied to multiple damage locations. Also, the results of the ULS curvature method contain less noise than that of the results of the mode shape curvature method. Finally, the mode shape curvature can pinpoint damage locations even with one of the lower mode shapes of the structure and it does not require the mode frequency.