Bridge health monitoring has been attempted to ensure the safety of the bridges in their operations, employing various measurement options like acceleration, strain, displacement, etc. The relative efficacy of these measurements as a damage-sensitive response has remained a topic of research. While acceleration has traditionally been used in abundance, dynamic strain, being relatively cheaper to record, also holds the potential to replace acceleration. This study undertakes a comparative investigation weighing the relative benefits of both the measurement options for prompt and reliable damage detection in both the time and frequency domain. The comparison is drawn in the light of damage sensitivity, intensity and consistency of the damage signature of the adopted measurement type while keeping the damage and loading specifications unaltered. A multi-span concrete box girder has been replicated with a high-fidelity numerical model as a proxy for the real structure followed by an experimental validation on a propped cantilever beam. Acceleration and strain responses are measured and analyzed for different damage conditions. A rigorous sensitivity analysis is undertaken to compare explicitly the performance of both the measurement options. The results demonstrated superior performance with the strain response in time and frequency domains from consistency and intensity perspectives.