Ambient vibration sources in many prime energy harvesting applications are characterized as having stochastic response with spectra concentrated at low frequencies and steadily reduced power density as frequency increases (colored noise). To overcome challenges in designing linear resonant systems for such inputs, nonlinear restoring potential shaping has become a popular means of extending a harvester's bandwidth downward towards the highest concentration of excitation energy available. Due to recent works which have individually probed by analysis, simulation, or experiment the opportunity for harvester restoring potential shaping near the elastic stability limit (buckling transition) to improve power generation in stochastic environments—in most cases focusing on postbuckled designs and in some cases arriving at conflicting conclusions—we seek to provide a consolidated and insightful investigation for energy harvester performance employing designs in this critical regime. Practical aspects drive the study and encourage evaluation of the role of asymmetries in restoring potential forms. New analytical, numerical, and experimental investigations are conducted and compared to rigorously assess the opportunities and reach well-informed conclusions. Weakly bistable systems are shown to potentially provide minor performance benefits but necessitate a priori knowledge of the excitation environment and careful avoidance of asymmetries. It is found that a system designed as close to the elastic stability limit as possible, without passing the buckling transition, may be the wiser solution to energy harvesting in colored noise environments.