One advantage for a Nuke CV is most of its fuel tank capacity is used to support the combat air wing. As an example CV-67 USS John F. Kennedy carried 2.5 million gallons of DFM for the boilers and 1.5 million gallons of JP-5 for the aircraft. A Nimitz class CVN carries 3.5 million gallons of JP-5 for air wing and about 500,000 gal of DFM for the emergency diesel generators, small boats and an occasional unrep for her escorts.
Underway replenishment for you non-Squids.