As chemical processes become increasingly complex and costs of experimentation increase, understanding the practical effectiveness of Active Learning methodologies is essential. In this regard, an ongoing debate is occurring within the research community about the use of Design of Experiments (DOE) and Bayesian Optimisation (BO). However, this debate is limited by the scarcity of systematic comparative studies. Therefore, this work provides a comparative analysis of two widely adopted data-driven optimisation approaches: DOE and BO. The comparison is conducted across two distinct case studies reflecting different levels of complexity, regarding the quantity and variety of input variables involved. The first case study represents a realistic in silico experimental scenario, with multiple decision variables of different types (continuous, categorical and mixture), and two distinct single-objective optimisation goals, while the second one considers a simpler, well-known benchmark model with just two input continuous variables. Both studies were designed and analysed, while acknowledging the inherent conceptual and operational differences between DOE and BO. The results showed that a sequential DOE strategy, adapted here for optimisation purposes, consistently outperformed classical BO under the tested conditions. Particularly in terms of convergence towards the target response, robustness in identifying the optimal region, and overall experimental budget efficiency. Rather than asserting the superiority of one methodology over the other, this work highlights the need for case-specific adaptation when applying data-driven optimisation strategies in Chemical Engineering. The findings emphasise that theoretical guarantees alone under relatively strict assumptions are insufficient and must be complemented by problem-driven evaluation to support informed decision-making.