The Atreus would destroy the Hades fairly easily. There's a difference between the Lucifer which is a technologically advanced, nigh invulnerable Shivan super destroyer and the Hades, which is a botched together synthesis of Terran technologies and half finished Shivan research.
We already know the GTI, as advanced as they were, couldn't field Kaysers which suggests their understanding of Shivan tech was pretty minimal. They were just using what they could and were able to salvage and reverse engineer.
Besides, the assumption is that the Hades is equivalent to the Lucifer. Yes, it might have Shivan beam weapons and some Shivan armour plating but Shivan ECM? Shivan ECCM? Shivan data capacity? The Atreus has fifty years on the Hades. That's fifty years of fighter advancements. Fifty years of ECM advances. Active armour systems. Advanced jump drives.
The Atreus could jump in at 15 klicks and launch its fighter compliment. The Lokis and Zeus wings aren't going to last long against TEI 2 fighters. Or it could jump in at two and rip the Hades apart with its pulse cannons. That is assuming the Hades can even hit the Atreus with all the EWAR suites switched on.
I see the modern GTVA warships as being partially derived from the lessons of the Hades. As numerically powerful as the Hades is, I don't see it lasting long against an Erebus.
