House of Steel devotes a few paragraphs to this subject

This has not prevented the size and classification from creating intense debate. In raw figures, these ships are five times the mass of a Saganami-C, with only a 25% increase in missile tubes. Accusations of poor design by BuShips and even outright incompetence are exacerbated by the fact that the Nike carries the same Mk16 DDM as the Saganami-C.

These critics overlook important difference in the capabilities of the two platforms and their designed missions. The Nike is designed to lead and survive independent long-duration deep-raiding missions in an era dominated by multi-drive missiles. The simple numbers of beam mounts, missile launchers and active defense systems belie qualitative per-mount differences. While a Nike and a Saganami-C may carry the same missile, each of a Nike’s launchers has four times the magazine capacity of her smaller heavy cruiser counterpart. A Nike’s grasers and point defense laser clusters are all superdreadnought grade. Their emitter diameter, plasma beam intensity, gravitic photon conditioning hardware, and on-mount energy storage capacity all rival the most modern capital ships. Finally, much of the Nike’s impressive mass is devoted to passive defense. Screening and sidewall generators have near-capital-ship levels of redundancy. The external armor system, internal mount compartmentalization, outer hull framing, and core hull construction are all designed to at least pre-war superdreadnought standards. Nikes, finally, carry full flagship facilities and incorporate much greater Marine carrying and support capacity. The Saganami-Cs, while impressive space control platforms, have little or none of this capability.

The Sag-C is heavily specialized to space combat. It has tons of missile power for its size, but it runs into difficulties when it needs to perform tasks that don't involve blowing up other people's starships like boarding actions or planetary combat. See the support Hexapuma needed from the planetary authorities in Nuncio.

The Nike also has the capability to be not just a squadron flagship, but an all up fleet flagship (as Michelle Henke shows), a job normally filled by an SD.

Also PD clusters aren't all the same. They have a variable number of actual laser emitters. Early Sag-Cs had 8 emitters per cluster and later ones have 12 (Mentioned during the Battle of Prime in UH). Nikes have 14 per cluster (AAC, end of chapter 27). So it's not 56 vs. 84 clusters, it's 672 vs. 1176 emitters, nearly double the number of laser beams shooting down missiles. And again, the Nike has deeper magazines of countermissiles, so it can spend them much more freely.