Alright, first, since GOT isn't my strong suit, tell me if a missed a group of peoples that would be a noticeable fighting force. Middle-earth is going to get serious leeway, but if you are on this wiki, you probably want to see LOTR win.
First, we have to calculate the troops available to all the GOT factions at the time of E1, S1. We also have to do the same thing with Middle-earth, at the time of Bilbo Baggins birthday, or the War of the Ring.
For this hypothetical matchup, let's say this happened: Kang the Conqueror decides to make two universes slug it out. The armies of GOT are transported to Middle-earth, located around Dale and in Palisor. They are given knowledge of the terrain, so it is still a fair fight.
For this, all evil and good LOTR factions ally. Screw relations, I can do anything I want.
Same thing for GOT. We will be seeing some White Walkers fighting alongside the brothers of the Night Watch, and the people of the Summer Island killing orcs along with the slavers of Ghiscar.
Now, for our factional strengths:
Hobbits, Bree-land: Sorry, guys. Cannon fodder and food producers for the war effort. Unless the Dothraki are stupid enough to not get to cover once a Bounder reaches for a stone to sling. Also, the Bree-men could get a enemy general drunk with Green Dragon ale, have him spill his secrets, and kill him.
Duendian of the North: Guerilla fighters. Good for picking off wights in forests. (I will get to the wight issue later.)
Blue Mountains, Durin's Folk, Orocarni Dwarves: These guys could go against the legions of the Westerlands and Reach. Despite the number crunch, they could be a formidable foe, although they would need to ally with other beings to survive. (Since the Orocarni Dwarves' numbers are open for debate, let's assume 20,000 or 10,000. Do you want LOTR to win this thing or not?)
High Elves, Woodland Realm, Lothlorien, Elves of Dorwinion, Avari Elves:
Absolutely devastating. These guys would destroy nearly any army, so lets put their skills to killing elite units, and the Unsullied. Those warrior eunuchs would at least match the Elves, but they would not be able to crush other armies of Middle-earth, assuming that the situation was favorable for the LOTR fighters. However, the reduced numbers of elves compared to the Unsullied could be a big problem.
Gondor,Drudain: This kingdom of men could go against the forces of the Arryn Vale, yet they would still be a strong force, able to have a navy, rangers, levymen, and footsoldiers. However, they probably would never be able to stand alone against most military-crazy GOT factions.
Rohan: These guys and Gondor could be a devastating force. However, the Dothraki would crush them, sadly. But this could be averted by...
Wainriders: If these guys fight with Rohan, the Dothraki hordes could be stemmed. Put things like chariots into the mix, and the Dothraki may be equaled, in skill if not in numbers.
Dorwinion, Dale, Woodmen, Beronings: Basic footsoldiers, for fighting against the Riverlands or Stormlands or whatever. The bows of Dale could do devastating damage. These guys would be able to match some of the Free Cities, with help. Turning into a bear is nice, but not if 10,000 Braavossi warriors are charging at you.
Fangorn: The ents would be good fighters, along with the Huorns. It seems cruel to force them to fight, though. Lets just say that not one man of Westeros or Essos would survive a couple of steps into Fangorn, although the war machines of the Westerlands and Crownlands would swiftly eliminate the Ents.
Lossoth, Taurthrim, Dunlendings: The Lossoth and Dunlendings can unite against the Free Folk, making a even match. Even if the Wildings won, there would hardly be any left. The Taurthrim a very numerous, but not united. However, in this hypothetical conflict, they are extremely united, and a cohesive fighting force. Also, they have a weapon that the forces of GOT will never expect: Millions and millions of weapons made of dragonglass!
Mordor: 500,000 orcs and evil men will crush most of Westeros. If this goes well, the GOT forces will be all dead before the good fighters can even arrive. If necessary, put them against the Dothraki, and the stronger, wealthier Westeros factions. This seems like a win-all for Middle-earth, but I will be using some exotic, book-only GOT factions to lessen the deadlock, and the Wights will be deadly to Orc-hordes. But I think that Suron may still have some masterly over ORc-wights? Unknown outcome.
Gundabad, Mountain-yrch, Moria Orcs: Here, we have a massive force of basic, unskilled orcs. About 200,000 or 100,000 thousand, I suppose. Let's put them against the North.
Dol Guldur, Angmar: Skilled, organized, deadly force. 40,000. Put these guys against the free cities, especially Qohor with all the Unsullied. And the spiders...
Isengard: A amazing force of strong and numerous soldiers. Put them up against the Free Cities, again. Maybe Yi Ti?
Half-Trolls: If organized and controlled, a exceedingly powerful force, if less numerous and far-removed. Put these guys up against the Unsullied or the Iron Islands.
Morwaith: Very numerous and unorganized. With the main issue of disunity gone, these could be basic soldiers to fight of the Free Cities, or possibly Wight-hordes. I say about a half million in all, at the most.
Limwaith, Cerinrim: I'm cheating now, aren't I? But what a advantage it would be to have exploding termite throwers on the LOTR side!
Near Harad, Variags: JEEZ, there are alot of these guys. Umbar to fight the Iron Islands, Coast Southrons as foot soldiers, Nomads to fight Dorne, I guess, and Gulfings as foot soldiers. Harrenor guys as foot soldiers again. Variags as calvary? Against Dothraki, maybe. And the Mumaks would be pretty good fr squishing large numbers of Westorosi...
Rhudel: This faction is almost unfair for the GOT crew. Fire throwers, samurai, endless legions...oh, well. About 100,000 skilled troops. Those wights are going to get fried...
Other unannounced future factions for Rhun: Many, many troops. Just sprinkle them in the legions of Arda.
Utumno: Kidding. If these guys counted, the GOT guys would be torn to dust before they could ring their warhorns.
Lesser forces, yet still formidable heavy-hitters:
Balrogs: At least two or three, with Durin's Bane among them. Shocking, and only magic wielding GOT guys could fight them. Melisandre...possibly.
Nameless Things: I won't count them, as they are more like animals that a fighting force.
Dragons: There are certainly more dragons in Arda in the Third Age than the three that Dany has. The Cold-drakes would be less effective, but Smaug's descendants (if he had any) would be pretty strong.
Istari: The Five Wizards could fight the White Walkers, Children of the Forest, Warlocks of Assai and Quarth, and other magic dudes. Not all of them at once, of course, but Gandalf versus Melisandre would be interesting to see.
Palantir, Rings of Power, Nazgul:
Palantir for speedy comms among Middle-earth forces, the respective powers of the Three, and the Ulari would strike absolute terror into the hearts of the GOT armies.
Eagles: Who knows? Maybe sporadic, powerful fighters.
Wargs: Countless wolves and wargs could provide mounts for orcs, and be standalone fighters.
Sauron: Very, very powerful. He could equal the Three-Eyed Raven in terms of prescience and knowledge, and would be far mightier. Sauron in physical form versus Night King?
Total Middle-earth strength: Two point one million, tops. Nearly unstoppable and would win (with very, very severe losses) if it were not for the Wights.
North: About 60,000 varied fighters. Could definitely equal or beat Gondor, and are not to be trifled with.
Crownlands: 10,000 fearsome warriors controlled by Robert Baratheon.
Stormlands: The Five Kings could field a army of 25,000 troops, including navy,
Reach: 100,000 powerful warriors. Not enough the equal the legions of Mordor, but enough to route the whole Morwaith force, or could beat Isengard in a direct fight.
The Westerlands: A combined 60,000 warriors. Absolutely devastating, so Mordor or Rhudel better clean up these guys quickly, if they want to save to field.
Dorne: House Martell should have about 20,000 available troops, mostly civvy conscripts.
Iron Islands: A incredibly formidable force. 20,000 skilled troops would route the forces of Arda. Sadly, they wouldn't last long against Elves or exploding termites.
Riverlands: About 35,00 troops. Footsoldiers, could definitely match Angmar individually, or maybe Dol Guldur.
Dothraki: 40,000 mounted. One of the most dangerous threats on the GOT side. Too many for Rohan to destroy, although the Wainriders could be a contributing factor to their downfall. Relatively unskilled, but fearsome.
Free Folk: In season one, the entire fighting force of Wildings was 80,000 unskilled tribesman, including giants, Thenn, and Mammoths. They couldn't stand against the Taurthrim, but the Lossoth and Dunlendings better watch out. (Lossoth get war mammoths too, so add that to the Arda advantages.)
Aryn Vale: 35,000 mounted knights. Could be evenly matched with Gondor and Rohan together. However, with the exception of the Rohirrim and Dothraki, mounted soldiers always equal just as much with ground soldiers.
Riverlands: 15,000. A lesser force, as the constant wars in the Riverlands spend a lot of blood.
Free Cities: 100,000 warriors, of varying skill and specialization. Put these guys against Rhudel or Haradrim, and it shouldn't end well for both sides.
Unsullied: At the very, very most: 10,000. I would like to see how the ELves deal with these guys.
Summer Islands: A rabble of tribes to fight the Morwaith.
Asshai: About 2,000 magic wielding warriors. These guys would be devastating, (but could be matched by my personal non-canon faction, Mossia.) and Gandalf would have a issue dealing with these guys. But the comparatively lesser numbers would be a big issue.
Yi Ti: 200,000 trained troops to match Rhudel. This almost completely turns the tide for the GOT side, if not for Rhudel.
Warlocks of Quarth: Who even cares about these guys? Isengard would just destroy them.
Faceless Men: Impeccable assassins. Aragorn, watch your back...
Children of the Forest: The Nazgul could take care of these guys.
Stone Men: I don't know about these guys. Considering that they infect everyone they touch, and are little more than unorganized animals, it doesn't seem like they could be used by GOT, for heath purposes. If they were, the Greyscale Plague would spread like wildfire, which brings us to our next weapon...
Wild Fire. Minas Tirith would not do very well against this stuff. But Khamuls Fire could cancel it out, or have a similar effect.
Wargs: (Not the wolves.) Trained Wargs could predict the outcome of events for the GOT side. But Gandalf can beat them, we know he can!
And the big thing we have all been wondering about...
Night King and Wights: At the start of the show, I would say that they have a maximum of 10,000 wights at the time, but numbers eventually become irrelevant with being able to raise the dead.
I am assuming that the Istari or Sauron could kill WWs, and the millions of obsidian weapons distributed by the Taurithrim would give a advantage to the Forces of Middle-earth. However, this depends on a lot of factors.
Orcs operating war machines and Khamul's Fire would be pretty devastating to the Wights as well.
Total GOT fighting force: about a million and two thirds. However, the wights are really the only thing that matters here...
So here is how the war would go:
Gandalf and Sauron, with a army of Taurthrim, quickly kill the Night King before the numbers of Wights can swell the force of the GOT army.
Using a variety of guerrilla and standalone battle tactics, the GOT forces are exterminated, but Middle-earth is decimated. No one can really win in this.
Scenario two: The Night King manages to survive, and the wights spread out of control. Most of Middle-earth is annihilated, but also the GOT armies too. The only real winner in this situation are the Others.
Scenario three: GOT forces mostly win, until the armies of Middle-earth come to a standstill at Minas Tirith. THe field looks lost, until...
Aragorn arrives with the Dead Men of Dunharrow, and destroys all the other GOT forces, with fear, (books) or actualy weapons. (movies)
Fourth scenario: Any number of billions of possibilities. I think GOT would usually 'win,' but either side would have a pyrrhic victory, unless Middle-earth had the forces of Utumno or Morgoth, or the GOT side had the Army of the Dead do all the work. (Getting lucky, in essence.)
Please comment! Did I miss anything?