Redundant robots operating in dynamic environments necessitate effective obstacle avoidance to ensure safe task execution while satisfying physical constraints. However, existing optimization-based obstacle avoidance (OA) methods, particularly the widely used variable-magnitude escape velocity (VMEV) method and the control barrier functions (CBFs), lack a systematic performance comparison across different quadratic programming (QP) solvers, limiting their practical deployment in real-time applications. This paper presents a comprehensive comparative analysis of CBFs and VMEV methods for these systems. CBFs provide formal safety assurances through forward invariance of defined safe sets, while VMEV employs adaptive escape velocities to separate robot critical points from obstacles. Both approaches can be implemented as QP formulations that combine a primary path-tracking task with obstacle avoidance and joint limit avoidance (OA-JLA). Performance is evaluated using six QP solvers: LVI-PDNN, 94LVI, E47, qpOASES, OSQP, and QUADPROG. Simulations and experiments conducted on a Franka Emika Panda robot demonstrate that the CBF method achieves improved computational efficiency, with an average solution time of 5.72 s compared to 87.69 s for VMEV in successful cases, resulting in a 6 through 20 times reduction in computation time. The CBF method attains 100% success across all solvers, in contrast to VMEV, which succeeds only with LVI-PDNN, 94LVI, and E47. Furthermore, the CBF-based OA-JLA framework yields smoother trajectories. These findings indicate the suitability of CBFs for real-time applications, particularly when paired with solvers such as 94LVI, which requires 3.11 s of computation time while ensuring safety guarantees.