I'll try my best to state how each match up will fair. Please feel free to argue any points.
Grunts vs. Wretchs
Both always comes in squads, with grunts led by an elite or brute.
All things considered, a grunt squad led by a leader can beat a batch of wretches, but this match up will take into account a leaderless grunt squad
Wretches have an advantage of being able to come from pretty much anywhere that they can fit. A single wretch can surprise a grunt squad and pick off a few as they panic. It won't survive the encounter, but since this won't be a 1 on 6-or so battle, the wretches have the advantage.
Winner= Wretches
Hunters Vs. Berzerkers
A deceptively complex fight.
Hunters always fights in pairs, while a berserker may have some handlers, who would either be ripped apart by the berserker herself, or prove to be nothing more than a nuisance to the hunters.
Both are pretty much armored, so won't fall to the first hit. Both should be of equal strength, with the berserker possibly being slightly stronger.
Berserkers have only their fist and strength, while hunters have a shield and energy based fuel rod cannons.
Conceviebly, the fight would happen with the berserker charging under fire from the hunter. The berserker would bash a hunter, knocking it down but not killing it. The berserker would then start to maul the downed hunter while the second hunter continues the fire or charges the berserker himself. The combined efforts of the hunters, with the use of their energy cannons, will barely but surely bring down a berserker.
Winner= Hunters
Elites Vs. Drones
Elites can include all of their ranks, including spec ops, honor guards, and most importantly, arbiters, while Locust drones can include Theron guards.
If all that bulk is indeed muscle, then the drones are physically stronger than elites. But elites themselves are stronger than humans and are a warrior race, plus are taller than drones, so they can hold their own in a fist fight with a drone.
Elites are more organised than drones and are far more technogically advanced. Elites hold an advantage in virtually every aspect you could hope for in combat, including a shield, energy weapons, cloaking and motion sensors.
A drone holds the advantage by surprising encamped or marching elites with emergence holes, a surprise that is quickly lost after the battle actually begins. Drones are also resilient enough to shrug off pain and persistant enough to lose "100 drones to kill a single fortified foe". But it doesn't matter how much pain a drone can withstand, losing a leg is still losing a leg, and losing 100 soldiers to kill one enemy is means you'll lose in a battle of attrition.
Winner= Elites
Brutes vs. Boomers
Boomers can include Mulchers, Maulers, and Butchers. Brutes can include Brute Chieftains. Boomers and co. are nothing more than large dimwitted meat tanks. Brutes are slightly smarter and have access to everthing Elites have, but lack the cunning in battle to effectively use them to their fullest potential.
Brutes are likely to charge into maulers or butchers waiting cleaver/flail. In the end, the deciding factor here is the Chieftains.
Being the strongest of the brutes, and the most "wise", they are a cut above any normal brute. Plus with a temporary invulnerability they can charge right through a boomer's or mucher's fire, and their gravity hammer can easily beat them to a bloody pulp.
Winner= Brutes
Scarab Vs. Brumak
First thought, even match up. Second thought, not so much.
A Brumak's strength lies in its firepower, size, and if need be, the terror is mere presence can impose on a battlefield. A scarab has it beat in all those categories.
A Brumak can have few passengers, all needed to control it and its weapons. A scarab can support an entire crew, most of whom are simply there to prevent raiding parties.
The only way a brumak can do significant damage to a scarab is if the brumak sneaks up on a scarab's blindspot, an unlikely event, and unloads with its weapons and claws. Even then the scarab can "kick" the brumak, blast it with the turret on top, or have the crew unload with plasma weaponry and plasma grenades.
Winner= Scarab
Tartarus vs General RAAM
Tartarus holds all the advantages of being a brute chieftain. RAAM won't be able to hurt him unless he is able to use a sustained fire until he breaks Tartarus' shield. If Tartarus manages to get close, he can smash RAAM with the Fist of Rukh (personnel gravity hammer).
The deciding factor would be how well lit the battleground is. Since RAAM would most likely have a plague of kryll to command, they could swarm Tartarus, even a shockwave won't keep all the kryll away from him.
Winner= Tartarus(bright/day) - RAAM(dark/night)
Arbiter vs Skorge
By "Arbiter", you are most likely refering to Thel Vedumee', the Elite you play as, and not the rank. As such this match up will be treated as such.
Since Thel was previously a Supreme Commander, the second highest rank an elite can obtain, he is obviously the one of the best elites period. He also has access to all elite tech and is known to be a skilled swordsman.
Skorge is taller than Thel, and carries a dual bladed chainsaw quarterstaff, has ink grenades, and is (possibly) physically superior to Thel. But having access to greater tech, including cloaking, means Thel has the advantage.
All things considered, nearly all arbiters should be able to defeat Skorge, not just Thel.
Winner= Arbiter
Locust Queen Vs Prophets (lol)
It's not known what the queen is capable of, if anything, and is seemingly only protected by a locust general, yet the High Proghets fight with special hover-thrones capable of producing a shield, fire lasers, and teleport, and Prophets are accompanied by higher ranked honor guard (elite or brute).
Winner= Prophet
In my opinion, those are the winners in those match ups. But in an all out war between the two, the covenant would win. They simply have far superior numbers (they are made up of over a dozen races, with the grunts species alone numbering something like 13 billion) and far superior tech (I haven't even gotten started on the vehicles or spacecraft)
All in all, the locust would put up a good fight, but they simply can't stand the might of the several advanced species.
The elites alone should be enough to beat the locust, let alone the entire covenant.