In Star Trek canon episodes dating back as far as TOS (ex.: The Enterprise Incident) and early TNG, there is an allusion made that Romulan technology in a lot of areas that are not directly tied to weapons and cloaking capability is somewhat more primitive than Federation technology. More advanced technology almost always yields a net reduction in volume for a given component.
Unfortunately, we're never told if the Romulans purchased the Klingon D7 Battlecruiser hulls from the Klingons, or if they were manufactured by the Romulans under contract, or if they were a blatant rip-off of what they saw as an excellent design for a combat vessel (similar to the way the Russians ripped-off of the design of the B-29 Superfortress). However, it almost doesn't matter because the mere appearance of those hulls in the Romulan historical inventory strongly suggests that the Romulans found their non-combat ship systems to be vastly inferior to those of their Federation counterparts. Considering the Federation's focus on broad ranging scientific advances in all aspects of starship engineering, it is highly unlikely that even if the Romulans were engaged in wholesale theft of federation technology that they would be able to maintain technical parity in engineering systems deployed in contemporary vessels.
If I had to guess, I would say that not only does the Federation typically deploy the most advanced propulsion systems (routinely outrunning or outmaneuvering same-class Romulan vessels), it probably also deploys the most advanced structural integrity fields and inertial damping systems to go along with it.
Matter Antimatter Annihilation (MAA) vs Singularity:
MAA amounts to storing incredibly dense potential energy in a fuel form where the fuel is produced elsewhere (ex.: a starbase), or is produced by the ship's own fusion reactors when not running at warp speeds. This is similar to the way a hybrid car powers the drive system from batteries that are constantly being replenished by an internal combustion engine.
Conversely, using a singularity is more like harvesting energy from a natural source that is difficult to initiate, control, and even shut down. Although it's a bunch of speculative technology, the analogs in current energy capture technology indicate that a harvesting approach almost always requires larger volume, low density systems, whereas a fuel based approach can be extremely energetic in a small, high density volume.
If the analogs in fuel generated energy vs direct harvesting of energy from a natural phenomenon holds for the Romulan singularity power source, that alone could explain why the D'deridex is so much larger. A good portion of it's internal volume may be devoted to initiating (no small feat that), manipulating (again, probably harder to do than with an MAA approach), and subsequently harvesting energy from a singularity. It could be that those volumes are needed to achieve similar performance to that of a much more compact and considerably less complex Federation MAA system.
Klingons and Romulans focus heavily on offensive, defensive, and maneuvering systems. In those areas they tend to excel, which is to be expected of races that perceive their warrior castes to be the foundation of their civilizations. In these areas, it is to be expected that their technology would match or slightly exceed the performance of their Federation counterparts.
Romulan ships, in particular, seem more dependent on physical structures within the ship to maintain structural integrity instead of using energized structures like Federation ships. Their vessels seem to all make use of either broadly distributed structures with opposing structures to balance them, and relying on considerably more bulky structures for smaller scales.
If the observation holds true, this fact alone would dramatically increase internal volume of virtually any Romulan vessel, even if the mass was close to the same as a comparable Federation vessel. This is due to the fact that wider spaced spars in any non-energized or low-tech lightly energized structure will have better moments of inertia and sheer resistance than trying to bulk up and strengthen a tighter, closed, non-energized or low-tech lightly energized structure. You could almost use the differences in the design approaches between a deep sea submersible (Federation energized structures) and a suspension bridge (Romulan non-energized or low-tech, lightly energized structures) as an illustrative metaphor. It may even been that having to rely on a larger, less dense structure is what made it practical for the Romulans to employ a singularity in the first place.
Also, it might be impractical to maintain intertial damping fields over the larger volumes this implies, which might mean that large portions of the internal volume of a D'deridex may not habitable while the ship is maneuvering inside a warp field, which would explain why the large volume does not correspond to a proportionally larger crew complement or evacuation capacity.
Lastly, Federation weapon systems seem to have always been more compact than those of their counterparts. Comparisons between photon torpedo tube bays between the Klingons and Federation make that very evident. The large size of Klingon disruptors in comparison to Federation Phasers (From hand held all the way up to bird of prey deployment) is very evident. Romulan plasma weapons have also been alluded to as taking up a great deal of internal volume, possibly making use of large numbers of low-density, high-energy, capacitor-like modules.
Taking all of this into account, it is a lot easier to see why a D'deridex might need to have so much more internal volume compared to a Galaxy in order to achieve comparable performance.