Most real-world optimization problems have multiple objectives and constraints. To address constrained multi-objective optimization problems (CMOPs), researchers have proposed many constrained evolutionary multi-objective optimization (EMO) algorithms. They usually evaluate the proposed constrained EMO algorithms on artificial CMOPs in the literature. As a result, some newly specialized constrained EMO algorithms are designed for those artificial problems. Our previous work demonstrated that an old EMO algorithm NSGA-II with a simple constraint handling mechanism can outperform some newly proposed algorithms on real-world CMOPs. In this paper, we further examine the performance of constrained EMO algorithms on artificial and real-world CMOPs. We also analyze the relationship between algorithms’ performance and problems’ properties.