The Empire still wins with sheer logistical strength. It can simply produce, move, and distribute equipment and personnel far faster and in greater numbers than the Covenant can. Their intelligence agencies are also efficient, unlike the Covenant's (from what I've seen.)
There's more to war than just having a bigger gun.
It's the Lucas happy-go-lucky BS that they won. In any case, the galaxy was better off with the Empire. When it collapsed (for lack of leadership, which I also find BS (no contingency plans!!!!!!1!!11!one!)), a power vacuum emerged and the galaxy went to hell like Somalia in 1991.
I assume this would be a battle against the modern day humans of the Halo universe? Because if it was a battle against the Forerunners it would be pretty one sided. Or heck if it was a battle against the Precursor's it would be a flat out genocide.