The size of the fuel cell and battery of a Fuel Cell Hybrid Electric Vehicle (FCHEV) will heavily affect the overall performance of the vehicle, its fuel economy, driveability, and the rates of fuel cell degradation observed. An undersized fuel cell may experience accelerated ageing of the fuel cell membrane and catalyst due to excessive heat and transient loading. This work describes a multi-objective design exploration exercise of fuel cell size and battery capacity comparing hydrogen fuel consumption, fuel cell lifetime, vehicle mass and running cost. For each system design considered, an individually optimised Energy Management Strategy (EMS) has been generated using Stochastic Dynamic Programming (SDP) in order to prevent bias to the results due to the control strategy. It has been found that the objectives of fuel efficiency, lifetime and running cost are largely complimentary, but degradation and running costs are much more sensitive to design changes than fuel efficiency and therefore should be included in any optimisation. Additionally, due to the expense of the fuel cell, combined with the dominating effect of start/stop cycling degradation, the optimal design from an overall running cost perspective is slightly downsized from one which is optimised purely for high efficiency.