Selecting appropriate ansatz topologies for variational quantum algorithms is critical for NISQ-era success. We present a quantitative comparison between two design paradigms: the heuristic Quantum Approximate Optimization Algorithm (QAOA) and an automated Quantum Neural Architecture Search (QNAS) approach for the max-cut problem. Our analysis is based on three indicators: approximation ratio, complexity, and optimization time. The results show that QAOA achieves a 25% higher average approximation ratio at the cost of a complexity 24 times higher than the one attained by QNAS. We note that this trade-off is dependent on the graph topology used for the max-cut problem. While QAOA achieves superior approximation ratios under ideal conditions, QNAS’s 24 \(\times \) complexity reduction suggests potential advantages in resource-constrained deployments—a hypothesis requiring validation under realistic noise models.