Power plants from fuel cells run on bio-fuels have been around for many decades (1950's-60's)... In actual use as power generation plants for civilian (niche commercial) as well as military applications!
Making them small enough for traveling soldiers has been an ongoing research direction for quite some time...
The biggest problem is actually heat - bio-fuel based fuel cells produce more energy/density than H + O systems (nature has stored more energy in the hydro-carbon chains)- but the cost to extract is high operating temps. While some of this heat energy can be recycled for more power the problem is reliable materials, safety and portability.
From a range/power available standpoint they can't compete with nuclear - but from a materials handling, safety, expertise, operating cost, and environmental approach they are a good fit for submarines and spacecraft. The tech to operate is actually lower, while the tech to create (practically) is higher.
Fuel is also more readily available at lower tech (than refined radioactives) and obviously safer and easier to handle (in general), acquire and, in a pinch, create.
On a starship, for the power - nuclear, even with shielding is likely to consume less space and will definitely consume less space for fuel.