Based on what we've seen in Blue Planet so far, I'd say we have a pretty good idea what exactly the Hyperion is and why exactly it is useful.
The Hyperion isn't meant to be a hard target assault platform, unlike the Chimera, Bellerophon, and Titan warships with their devastating forward firepower, despite their frontal cannon configuration. During the forced entry of the unknown Knossos portal in N362, the Hyperions were used to spearhead the assault - destroying the formidable, and similarly equipped and sized Rakshasa class combatants and waves of fighters, before more valuable and more in demand assets ran the gauntlet. In this sense we see Hyperion combatants used similarly to the Aeolus - as anti-fighter gunboats, only with the added advantage of being effective against similarly scaled opponents. During the destruction of the Sathanas class warship by elements of the 14th battlegroup ("A Time For Heroes"), not the Bretonia, Duke, nor Persephone participated in the direct assault. It can be safely presumed they which they were escorting the logistics ships Solace and Fortune - they would have been, in fact, the only vessels escorting the fragile logistics ships.
We have seen them used successfully supplementing the firepower and area defense of large fleet maneuvers - the Elissa and Utica both participated in the attack on Artemis station, and the captain of the Nelson even ordered his fighter charges to ". . .spearhead our assault against the Tev cruisers. Punch a hole for us to the Atreus." - the cruisers were suggested to pose a serious threat to a Karuna class battle frigate- a vessel that must surely be the mass of four Hyperions.
We have also seen the Hyperions class Courage and Novikov destroy the Bandersnatch, a soft target. They completed their mission without escort, using only energy based weapons in an environment where nearly all deploy-able assets were deployed - in short, doing the job of several wings of bombers, under the cover of a significant and effective anti-fighter screen. There is an excellent chance that they even completed their mission at much less expense than an equivalent force of bombers would have. Hyperions, in other words, can perform the task of assaulting soft targets - be they space stations, freighters, or gas miners, more than adequately, while sill leaving the big guns of larger assets free to destroy imminent and hard armored dangers. We have seen the Hyperion combatant fall short once, during the defense of the GTL Agincourt, when it was confronted with two full squadrons of Federal fighters and two Karuna frigates - during the fighting a Chimera corvette, a combatant who's utility has almost never come under question, also fell to overwhelming force.
In contrast we have seen Aeolus' in only one role in the Blue Planet saga, that is the role of anti-fighter gunboat. The Cho, during the assault on the Akula and Ranvir, offered little or no anti-capital firepower and failed to intercept three Uhlan fighters that made entry only a hundred meters from the vessel, a failure by most standards. The Essex and Ajax also fell easy victim to Federal fighter squadrons - during their escort of the destroyer Meridian. The jump-five assigned Norfolk definitely demonstrates that a fully prepared Aeolus combatant is easy prey to the federations Uriel squadrons. The Aeolus is not only a one trick pony, it is a one trick pony that is less than half as successful at its intended role as the Hyperion is at its own (larger) role.
