My vote goes for Star Wars, purely on a fanboy level before considering the facts. To be fair, Halo doesn't even deserve to be compared to Star Wars. I'm not saying that SW is the greatest piece if sci-fi ever created, gods no, but Halo doesn't even come CLOSE to it.
And really, how can you say for sure what Covenant plasma can do to Imperial shielding? Is there any record of plasma weapons being used vs those shields? And the reverse holds true as well, we have no idea how effective a battery of turbolasers or even the extremely powerful cannons on the broadside of a Star Destroyer would be vs a Covenant ship.
As for ground battles, I'd like to see a Banshee try and take down an AT-AT. And the Rebels would have no problem in taking down a Scarab, as they'd approach it exactly how they approach taking down the aforementioned AT-AT.
The OP said that he couldn't see any reason why the Rebels would fight side-by-side with the Imperials, but if the Covenant showed up in the SW universe, and even if the Imps and Rebels didn't team up against them, they'd be fighting a war on 2 fronts. Looking at our own history tells us that this is not a situation you want to put yourself in. Yes, we know that parts of the covenant, the ones that split off from the prophets, would and have allied themselves with the UNSC, but I'd say it's a fair bet that if both UNSC and Covenant showed up in SW 'verse, the UNSC would join either the Imperium or Rebels. It's human nature to join with other humans to fight a foreign enemy while we're not fighting each other.
As for comparing actual troops, the Storm/Clone Troopers are not as clumsy and bad as they are shown in the films. In fact, they're an extremely competent fighting force. They weren't able to wipe out the Jedi by being absolutely awful, were they? The rebel ground troops aren't that great to be fair, and then you've got the droid armies...thinking about it, against the covenant's selection of aliens from a small amount f planets compared to the Star Wars universe's several different star systems of factions, they'd be hard pressed to take any planet, other than simple ones like Tatooine. Outer rim is about all they'd get and even then they'd get the fight taken to them. The ground war would be won by Star Wars, due to sheer numbers.
And if we ompare the elite troops? Spartans, brutes and elites up against Jedi, Commando Clone Troopers, super battle droids? Yeah, we know where this is going. 'sabers can quite possibly deflect or absorb the covenant's plasma, and getting close enough... Commandos, SBDs, all going to put up a fight but I reckon they'd lose out to the Halo elites. Only jedi/sith are going to beat them.
Back on the subject of the space war, I direct you here. http://stardestroyer.net/tlc/
Essentially, what you need to know from there is that a turbolaser shot puts out around half the power of the Hiroshima bomb. Now take into account that each turbolaser can fire say, once per second and that there are many, MANY turbolasers per star destroyer...goodbye covenant battle cruisers and what have you.
Would you like some asprin for that, Halo? Perhaps a plaster? Pretty bad flesh wound, that...