Modern aircraft carriers have thousands of people on them and their volume is comparable to the E-A.

they also don’t need to run completely self-contained life support systems that must generate and maintain water and breathable air rather than pulling it from conveniently free (or near-free) sources right outside the ship

The energy requirements for warp travel are also many orders of magnitude higher than pushing a carrier through water so the space dedicated to warp cores and other energy management/propulsion systems must also be greater