The development of digital bioprocessing technologies is critical to operate modern industrial bioprocesses. This study conducted the first investigation on the efficiency of using physics-based and data-driven models for the dynamic optimisation of long-term bioprocess. More specifically, this study exploits a predictive kinetic model and a cutting-edge data-driven model to compute open-loop optimisation strategies for the production of microalgal lutein during a fed-batch operation. Light intensity and nitrate inflow rate are used as control variables given their key impact on biomass growth and lutein synthesis. By employing different optimisation algorithms, several optimal control sequences were computed. Due to the distinct model construction principles and sophisticated process mechanisms, the physics-based and the data-driven models yielded contradictory optimisation strategies. The experimental verification confirms that the data-driven model predicted a closer result to the experiments than the physics-based model. Both models succeeded in improving lutein intracellular content by over 40% compared to the highest previous record; however, the data-driven model outperformed the kinetic model when optimising total lutein production and achieved an increase of 40-50%. This indicates the possible advantages of using data-driven modelling for optimisation and prediction of complex dynamic bioprocesses, and its potential in industrial bio-manufacturing systems.