I like how descriptive your post was, it lets me think more about the topic at hand.
I would definitely say FF12 and 13 has the better military, but I would say through technology and machines.
I mean, if you were to remember the Havoc sky tank boss, you might also remember there were 2 more ready to fight you. They could just spam them and probably win, add some more Proud clouds and some of those subjugators and there is a big problem.

And FF12 really has the definitive advantage when it comes to airfleet.
But remember that the sanctum also has "beasties" for them. The ishimal subjugator, numerous flying beasts with the advantage in flying ability, and the warp gates for beasts. I am not sure, but what about Bartandelous?(spell fail)

Ah yes, and about SeeD. I do not think they are really advance when you look at them whole, but if you consider, that the SeeD in Galbadia, work for the Galbadian Army, you can add them to the galbadian army.
They do have those weird air hovering things. The ones the galbadians used in the attack on Balamb. Now, there is also the missile base, which is the Galbadian missile base, which should be counted on their part as offense. If they can spam missiles from from a distance, that can assure a cheap victory, or at least increase their chances.
They also are tinkering around with machines as well, remember the machine robot? The one with all the damn letters and numbers in the first seed mission. And the blue machine you fight at the missile base.
I will say it is too bad Esthar's military power wasn't shown, as I feel with Adel, and ragnaroks, they could have a decisive lead in this category.
I am not sure about this next one, but what about the Lunatic Pandora? The galbadian army got ahold of it and used it to summon a lunar cry, which can outweight most soldeirs.

I guess the Galbadian Army in themselves are a good canidate.
I like your desisions.

How about in this format.

Best...
Aerial fleet.
Navy.
Ground force.
Tacticians.
Power.
Number.
Technology.

As for the aerial fleet, I would say it is between Archadia and Sanctum. They both have an impressive battling fleet. But in one cutscene in FF13, I feel as they showed a slight advantage in terms of prowess in their aerial fleet.
As for Navy, I will say FF5's Xexat Surgates Navy, only because I don't remember another FF with an navy.
Ground force for me is difficult. As for individual skilled persona's, I will say, it is between SeeD and the Archadian empire. SeeD which are highly trained at an early age, have Guardian forces, or at least the Balamb side does. Eden anybody? And I also placed Archadia because they have the tech to stop anything SeeD may potentially bring.

Tactically, it definitely goes to Archadia. I mean, all they showed, or at least their uppers, was extreme planning when it came to anything about war. I was going to bring up SeeD, but it was only the Main party and ocasional help from Laguna t the end who showed any type of Planning.

Now, here is a sketchy subject. Power. Alexandria has great power with Bahamut, Atomos and Myself. But other than that, as in pure destructive power, their fleet isn't as powerful. Galbadians have Missiles, which should be able to destroy anything it makes contact with. I believe they sent 12 missiles at balamb, and 12 more at Trabia. ANd from what we have seen, they have ALLOTS more. The Al-bhed have power in Machina. Their ship, or their creation, the Celsius, or the other measure of temperature, tore sins arms off and bore a hole in him, which to me is a great deal of power. The sky fortress Bahamut has that main cannon, which is a death ray on steroids. Sanctum never showed power in this sense, but they have allot of minor power.

Now, as for number, it is between Sanctum, Archadia, and emperor gehstals empire.
I will make it a draw between Archadia and Sanctum, as most of Cocoon is sanctum in a sense.

Now, Technology will go to FF13's Sanctum, maybe if Esthar showed more prowess in game, Io might had changed but, it is no contest here.

Overall, I will say FF12 and FF13 had the best Armies.
Now hwo about Resistance groups?