This study established a finite element model to assess the impact of various transverse strengthening techniques on the Xiuzhen River Bridge, a prestressed concrete box-girder bridge. On-site experiments validated the effectiveness of the finite element model. Five different strengthening techniques, namely, adding steel or concrete diaphragms (ASD or ACD), adding composite truss (ACT), strengthening bridge deck (SBD), and setting transverse prestress (STP), were compared. The results demonstrated a significant reduction in the deflection of the bridge using these techniques. SBD technology exhibited the highest deflection reduction rate at 47.91%, and STP technology achieved a maximum reduction rate of 53.92% in the presence of initial bridge damage. In addition, these techniques notably improved the lateral integrity from the load distribution factor (LDF). However, relying solely on the LDF cannot discern the most effective strengthening method. Therefore, a combined LDF and Kullback-Leibler divergence method was proposed to comprehensively analyse the relative entropy (RE) between different models. The results highlighted that SBD technology significantly reduced the RE of the bridge by 82.94%. In the presence of initial damage, ACT technology demonstrated significant stability in reducing the RE, with a sensitivity of only 10.98%. For newly constructed bridges, SBD technology is notably effective; however, for existing bridges, ACT technology may be a reasonable choice. Additionally, an investigation of failure modes emphasized that all the models exhibit similar failure modes, with initial damage and the implementation of different techniques primarily affecting cracking and ultimate load rather than significantly altering the overall failure mode.