Keep in mind that this is the entire halo universe. That includes all the rings, both arks, the forerunners, and the precursors/flood. I'd say halo has a pretty decent chance at winning.
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The flood have an answer in Orbital Bombardment. The rings need humans to activate them (or forerunners) but are a last resort in case everything needs to die. Force Ghosts also can manipulate things in the physical world on a very massive scale. What part of "more powerful than you can possibly imagine" does nobody get? In universe instances of Luke Skywalker's force ghost collapsing stars and remaking solar systems. Halo rings wouldn't exist for very long, especially considering the forerunners would not wish to use them giving any cohesive force a chance to neutralize them. The death stars (all 3) would be immaterial to the battle, as would the halo rings. Both sides have the ability to effectively negate any super weapon pretty much at will. I'd say the only real "super weapon" that would have any impact would be the Eclipse class super star destroyer. But that would likely get destroyed as well.
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The flood at its height had control of Ais and a vast former forerunner fleet.
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Still Force ghosts that can create star systems. STILL a race that can create, manipulate, and control black holes. Halo has 0 chance. The flood wouldn't survive. The forerunners wouldn't survive. the UNSC are hopelessly outmatched. The covenant couldn't handle it.
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The Vong can create black holes essentially eliminating rings from the equation.