Well, keep in mind, Alix, the Covenant Assault Carrier is second, only, to Supercarriers, Unyielding Hierophant (other ships of the class?) and High Charity, in size. There are Light Carriers, Corvettes, Battleships, Destroyers, Frigates, Light Cruisers, Cruisers, Supercruisers, and so on, within the Covenant armada. Maybe work with Destroyers, Corvettes, Assault Carriers, Battleships, and Cruisers (ships we've actually seen in Halo), and Seraphs for pawns. On the UNSC side, go for Marathons, Destroyers, Frigates, Space Stations, and Longswords, maybe.
I'll give you that Battlestars are fairly multirole, but they also appear to be the primary workhorse of the... Er... Humans? (It's been TOO long since I watched BSG) I did some research, and all UNSC ships carry Shiva nuclear missiles, the Marathon has TWO MAC cannons, 60-missile Oversized Archer tubes (unknown number of tubes; likely more than 300) an unknown amount of 50mm point-defense guns, and 2 meters of Titanium-A battleplate.
Battlestar (according to your new Re-imagining) has 24 heavy turrets, 514 point-defense turrets, 12 nuke tubes, and 4 20-Viper fighter contingents, as well as a handful of Raptors. The heavy turrets act more like missiles, according to video and their description, a la Galactica Wiki, so they fall under that category, and the rest just fits in place. Note: I found nothing about armor composition or structure, so I'm assuming it's not as heavily armored as a ship designed to combat slugs fired at a notable percentage the speed of light with SOME efficacy. We'll say 1 meter of titanium armor. Also, Battlestars are described as "a Colonial capital ship that combines the functions of an aircraft carrier and a battleship."
Anyway, based on descriptions of armament, a Marathon cruiser (Even Halcyon, to be honest) outstrips the combat capacity of a Battlestar, even accounting for the fighter wing. Even if you couldn't fire the MACs, the Archer missiles, in their massive numbers (60 volleys of 300+) would quickly overwhelm the point-defense ("mounted on the flight pods and other surfaces. Each barrel fires explosive rounds in bursts." <- can't make a cloud) turrets. Single Archer missiles are stated to be able to "disable all but the most heavily-armored UNSC ships." Imagining several get by the phalanx.... And this isn't to mention the single ships a Marathon carries, or its Shivas.
I'm sorry, but 50mm point defense vulcans (capable of continuous fire, rather than bursts) defeat missiles, from almost all angles, as well as a contingent of fighters that are that small, and the armor would likely not buckle under ship-sized flak guns. Let's just agree that UNSC cruisers are more heavily armed and suited to their role, and Battlestars aren't as armored, but more spacious and suited to their role. Again, you can't compare the two, as they serve different roles. It's like a machine gun and an air-to-air missile. They can dabble ineffectively at each other's work, but you can't really say one does the other's job better.
And, if the Galactica is less powerful than the Marathon (or the Autumn, if I can make Halcyons stick), then I wouldn't dare pit it against a Covenant ship of any class. (Though, if we were to weld a couple Frigates on, one on each of the flight pods.... I mean, its FTL is much more precise than UNSC...)
But, you do have a point. If I had to see it fight, I'd like to see it on the UNSC's side.