In this paper, we consider the meta-learning problem of metaheuristic optimisation performance prediction as a foundation underlying the task of algorithm selection for solving optimisation problems. The relative effectiveness of a problem-specific versus an algorithm-specific meta-learning approach is ascertained in the illustrative context of the celebrated knapsack problem. Leveraging the notion of fitness landscape analysis, our algorithm-specific approach incorporates neighbourhood structures induced by metaheuristic perturbation operators. Employing a random forest model, we conduct a comprehensive empirical analysis, contrasting algorithm-specific and problem-specific meta-learning. Two renowned metaheuristic search paradigms are considered—that of simulated annealing and that of a genetic algorithm—each with various hyperparameter and perturbation operator configurations. The numerical results provide insight into the cost-benefit trade-off between problem-specific meta-learning and algorithm-specific meta-learning. It is found that algorithm-specific information yields superior meta-learning performance, but incurs a greater computational cost during meta-feature extraction.