Here are the rules.
The Reapers are invading the Covenant before they first encounter humanity.
The Mass relays are in the Halo Galaxy.
Firepower and shields are equalized proportionally to their mass so two ships of equal mass will be equally powerful.
Please provide proof for your claims.
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In an all-out naval battle, the Covenant would probably win. Their ships are much larger, plus they can target the mass relays to disable faster-than-light travel for the Reapers, while retaining their own ability to make hyper-accurate slip space jumps. Plus, Covenant ships are equipped with insane energy shielding, hundreds if not thousands of plasma turrets, energy projectors that can scorch entire cities, and (occasionally) invisibility. On the ground, it would be a massacre. The Collectors and Husks have few advantages over the Covenant's soldiers. Reaper Brutes are easily taken out by Hunters, Collectors are outmatched by Elites, and Grunts can, surprisingly, deal extensive amounts of damage in large groups, especially when armed with explosives. There's not much the Reapers can do against a Scarab either. Reaper air superiority is easily countered by Covenant AA guns and Vampires. You can also look at how far each came when fighting humanity. The Covenant reduced the UNSC military to almost nothing and glassed the majority of Earth's colonies before the war ended, while the Reapers barely touched Earth before the Citadel races brought them down.