Covenant ships are bigger
Covenant ships have more powerful shields
Covenant infantry have better weaponry
50% of Covenant infantry has shields
Covenant is led by Arbiter
Empire has Death Star
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But the covenant just straight up has better weaponry. Needlers, needle rifles, fuel rod cannons, invisibility. Scarabs are like AT-ATs on steroids. Ghosts and Wraiths have incredible maneuverability advantages over empire ground vehicles. Also the different races give covenant infantry a plethora of different field tactics that they can enact against a group of storm troopers. I even bet a group of grunts could take a group of storm troopers. On average, covenant ship masters are better tacticians than imperial admirals as well, so they have a distinct ship to ship advantage.
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I was too lazy to reply sry. From reading both Star Wars and Halo books, I've just come to the consensus that shipmasters are just better. They literally spend most of they're life training and many are veterans of actual huge battles. The Admirals in Star Wars have just been eliminating far inferior rebels and pirates for the past decade. Darth Vader, a past general, comments all the time on how incapable they are as leaders and tacticians.