Let me make a few corrections...
Overall Size:
Covenant - Massive fleets, numbering in the thousands
Empire - Dozens of ships, millions of fightercraft
Winner - Close, but I think the Covenant get this one
The Empire has a fleet of 25000 Star Destroyers. That's in Canon universe. Add to that a indefinite number of support crafts, fighters, transport barges, navigation buoys, ecc.... You get the idea. That's far from the "dozens of ships". By VERY far.
Years in Existence:
Covenant- Eons upon eons of history
Empire - Two whole decades
Winner - Uhh...Covenant I think
Yes, true. Although the Star Wars Galaxy has been around for a long time too. Plus, as time passes, vast empires tend to become opulent, corrupt and generally decadent: that has happened in our history many many times. Plus, if you remember correctly, that's the very reason why the Empire was born in the first place. So, I'd say, in general, a "younger" organization is by far better: you can react faster and don't have the burden of a too spread out burocracy.
Best Space Machine:
Covenant - Giant cruisers, a fleet of millions, and a massive city
Empire - The Death Star
Winner - Empire. Come, on, seriously.
And then, they could build TWO of them.
Ground Vehicles:
Covenant - Wraith tanks, Banshees, Ghosts, and Scarabs
Empire - AT-STs, AT-PTs, and the Mighty AT-ATs
Winner - Empire. Just cause AT-ATs are sweet.
That's the only thing i don't like about SW. Yes, AT-ATs are a sight to fear on a battlefield (and in that they suit Moff Tarkin's Terror Doctrine). But still, blasting away a planet's resistance from orbit is far more efficient. The only reason the Empire used AT-AT in the Battle of Hoth was because Darth Vader wanted to capture prisoners. Otherwise, they would have been blasted long before that.
Infantry Units:
Covenant - Grunts, Jackals, Drones, Elites, Hunters, and Brutes
Empire - Stormtroopers. LOTS of Stormtroopers
Winner - Covenant, Stormtroopers die too easily.
Unless you can clone them = pretty much infinite "supply". And, last time I checked, the Stormtroopers where the elite among infantry. So, the majority of the engagements where dealt with by Marine Infantry, not by Stormtroopers.
Biggest Blunder:
Covenant- Can't kill a singular super-soldier who destroys their sacred ring
Empire - Built a thermal exhaust port that would convienintly destroy their best weapon
Winner - Tie. They're both retarded in that sense.
Oh well. That's because you need a story and some sort of gameplayability... Immagine Halo if the Covenant overwhelmed you 10000000/1. That wouldn't be fun, would it?
And, btw, there's one small difference. At the end of "The Empire Strikes Back", the Empire is actually WINNING against the Rebels. They are scattered off and hiding. A whole year passes before they can get back to action (in the Novelization of ROTJ, the actual time is six months, but I think we can agree that the dates we see in the movies count here). There's no such thing in Halo, at least, that I can remember. Master Chief is always on the Edge, never backing.
Evil Leader:
Covenant - Prophet of Truth; betrayed the Elites to fulfill the Great Journey
Empire - Emperor Palpatine; exterminated all of the Jedi to maintain power.
Winner - Empire. We all know the Emperor would kill you for no reason. Plus he's got lightning.
Uhm. If you say so

Coolest Warrior:
Covenant - The Arbiter; a Covenant holy warrior, kill the Brutes.
Empire - Darth Vader; Lord of the Sith, chokes people.
Winner - Empire. Darth will always win.
Oooooh yes

And the winner, with 4 to 3, is the Galactic Empire!
What do you think? Please share your thoughts.
So, I'd probably say the Covenant have NO chance. Not even in a long term attrition war.
In a military clash, there would be no contest. Empire would own the Covenant. However, in stability the Covenant takes the first place, even if the treason of Truth did cause a civil war within the Covenant. The Empire was short-lived and collapsed when its leaders perished, allowing the New Republic to take their place. Anyway, military-wise the Old Republic, Galactic Empire and New Republic form some kind of a contiuum. I think the military power of that combined history peaked in the Clone Wars at the time of the six movies. Sith Wars probablt caused even more military action.
Yes, you are correct. In a such vast galaxy, empires, political organizations, corporations, nations, planets, cultures, races can come an go in the blink of an eye, without the rest even noticing. In fact, there are places where the Empire (or of the Old Republic, for that matter) is not known of (the nebula beyond Nar Shadda, as an example). The only constant in SW is, no matter how far and remote, there's always someone wagin war on some other one. An external threat would do nothing else than bring together the biggest factions so that they can repel the common foe and go back to their fighting.
Mixing universes is fun and pointless.
We all are a little bit "nerdish" around here... so who cares?
