In this study, mathematical models are developed for a Microbial Fuel Cell (MFC) with a 'fermenter-Electrochemically Active Bacteria (EAB)' type, two-species biofilm, governed by Mediator-Based Extracellular Electron Transfer (MET) or Direct Conduction-Based Extracellular Electron Transfer (DET), and operating under a batch or continuous mode.Numerical simulations have been carried out to test the impact of a range of physical and biochemical parameters on biofilm composition and current generation.The results reveal the contrast between two operating modes, caused by the difference in the length of time available and in the substrate supply for the evolution of the biofilm, and the contrast between systems governed by MET and DET, arising primarily from the difference between the role of the mediator and that of the electrical potential played in the two systems, respectively. Many observations, including several counter-intuitive occasions, stem from the trade-offs between the impacts of the process parameters on bioelectrochemical kinetics, mass transfer, and electrical resistance. The simulation results also predict the existence of optimal parameter settings in various cases for the purpose of electricity generation. These findings provide potentially useful insights to guide the design and operation of MFCs or other types of bioelectrochemical devices that employ multi-species biofilms.