The official novelization of the ROTS film states very plainly that the common power generation technology in the Republic for starships and personal vehicles are "fusion furnaces" operating on the same basic principles as suns - i.e., nuclear fusion. Fusion provides up to ~800 terajoules per kilogram of fuel.Republic attack cruisers can take off, land, and take off again without refueling. If they have the ability to come to a full halt in mid-trip as well as fight and maneuver, this would suggest at least 2 gigajoules of available energy reserves per kilogram of ship; given a probable weight on the order of millions of tons, this places reactor capacity on the minimum order of 1018 joules.
A lightsaber may be operated for some time without requiring a recharge. A lightsaber may, in the course of a second, melt perhaps a meter long strip of metal. By reference, melting a 100x2x2 cm strip of steel would take a significant fraction of a megajoule of energy. If a lightsaber can put out that level of power for an entire hour, it would contain several GJ of energy.
It is unclear how long a lightsaber may be operated continuously, or if lightsabers have a constant output; this may vary according to the specific model.