Transportation electrification is undergoing a significant transitioning towards the utilization of efficient and reliable energy sources and smart integration schemes, where this transitioning is continuously facing ever-tightening challenges in order to comply with the increased environmental regulations. Among the different means of transportation, the global maritime transport is responsible for 2-3% of global greenhouse gas (GHG) emissions and it is predicted to increase to 17% by 2050 if no changes are adapted. Hence, the international maritime organization (IMO) has targeted to reach a 50% reduction in GHG emissions by 2050 compared to 2008. Hence, alternative energy sources shall be utilized in order to meet these strict GHG emissions reduction targets, where batteries and hydrogen-fed fuel cells can play a vital role in such aspect. Since the output of these two energy sources is unregulated DC voltage, their connection to the whole ship power system can be accomplished in several ways, where each way has its features, in addition to utilizing different power conditioning stages (PCSs), and these features are not well clarified and compared in the literature. Hence, this paper presents an overview of the possible integration schemes that can be utilized in fuel cells and batteries-fed vessels, which is supported with a comparative assessment. This is also presented along with highlighting the state-of-the-art PCSs that are available in the market and can be utilized in these integration schemes within marine vessels. Such overview and comparative assessment are seen to be of significant importance and added value for researchers and developers in both the academic and industrial sides in order to accelerate the adoption of fuel cells in marine systems for zero emission shipping.