Active learning (AL) promises accelerated multi-objective materials discovery, yet acquisition-function choice is often made without matching dataset, budget, and target metric. We retrospectively compared EI-random, EI-cent, EI-maxmin, and EI-prod on Al alloy, steel, and Cu alloy datasets across 100 randomized cold-start trials, using hypervolume, true Pareto-sample discovery, inverted generational distance, balanced-performance score, and iterations to 95% target. EI-prod is best overall on Al dataset; EI-maxmin improves Pareto-front recovery and convergence on steel and Cu datasets; EI-cent gives limited, inconsistent gains. No strategy dominates all datasets or budgets. These results provide a metric-aware, outcome-specific selection guide: use EI-prod for early balanced candidates, and EI-maxmin for broader Pareto-front exploration. They also warn that similar balanced performance does not ensure equivalent front reconstruction and that dataset-specific rankings should inform, not dictate, AL design in materials screening. This reframes acquisition selection as a decision-making, not universal-ranking, problem.