Covenant will always have the advantage when capturing hooks early game because of their leader unit. Until about 8 minutes into the game, nothing UNSC can build will win in a fight between them and a single covenant leader when fighting over a hook.

And even if you try to fight for that hook with some marines spartans, you're just wasting your economy early game against a superpower unit that costs nothing. You could build three spartans. 900 resources. And you'd still loose to the arbiter, BC or Prophet. And all they ahve to do is kill any rebels and teleport in a single uniquie unit and bam, hook captured. Unsc have to build some warthogs to kill rebel infantry and then some marines to capture the hook.

I guess that's proof covy have the advantage early game, at least UNSC get really good late game, if they can get to that stage.