Greetings!
Dragonblade! There you are!

Preach on, brother! Preach on! By all means, get that campaign goodness typed up!

It was such a blast!
The Lone Gunman:
Well, depending on the type of scenario being run, I do one of two things. You are onto part of it I suspect, in that there are two different *systems* as it were. For example:
When the group is in rather tight quarters, or say skirmishing with less than 1200 troops or so, I tend to do exactly as Dragonblade describes--I juggle it all in my head, assisted by some very detailed notes, as needed. This aspect of a scenario is crucial to understand, in that as one wants to embrace the ebb and flow of more than a small handful of people, like the party, and yet, something less than a full-scale army, this kind of skirmish action, in my view, requires a fast and furious approach, because what is more important is the story, the drama, the immediate sense of blood and death with decisions being made with imperfect knowledge with people being slaughtered in screaming death all around you. This allows the supporting troops--from several dozen or a few hundred, to a thousand or so, to have some realistic effect on the immediate battle, and at the same time allows the focus to be specifically on the party.
Now, the other type of scenario--say that of a set-piece battle between armies of hundreds of thousands of troops, or even millions, I use something like the Mongoose system from the back of their Quintessential Fighter book, with some modifications. I roll a D20 for each side, with each major unit being in a "fight" and add or subtract the various modifiers based on esprit de corps, numbers of troops, equipment, leadership, terrain, and so on. All of these conditions have some kind of modifier number, which is applied to the die roll, either positive or negative, which is cumulative. I do this for both sides, and the difference between the higher and the lower determines the overall percentage in losses, either dead or wounded. The larger the difference in that number will influence either a mass surrender, or a mass slaughter as one side fights to the last man. That seldom happens, but massacres can occur.

It isn't really a "scientific" system, but one that requires thought and interpretation on the DM's part.
For example: Army A of 800,000 soldiers is dug into fortifications, and heavily entrenched. The other side, Army B, has a force of 1, 800,000 troops. Army A rolls a 20, with modifers, making it a 38. Army B rolls, and gets a 16, with modifiers, making it a 28. Results?
With some other calculations in my head and a quick scan of some notes, Army A, the defender, would lose 50,000 troops, (25,000 dead/25,000 wounded)-- dead and wounded. Army B would lose 100,000 troops, mostly all dead, in the first day of battle.
I can make these assessments in about 5 minutes.
The point being for using this kind of system for roleplaying, is that one wants to capture the scope and sweep of a huge, epic battle, and be able to do so fairly quickly, without needing to bog the rest of the game or the story down in trying to simulate a mineatures wargame. A simple one page chart that I use I can determine in about 15 minutes the results of a huge epic battle between the two armies I described in a battle that may last from several days to several months of game time, but I can resolve it quickly, with many of the important calculations and details factored in, and done so in a smooth and elegant manner. This allows also for such to occur within a standard game session, and doesn't require any mineatures, game-boards, or what not. It requires careful thought and planning though on the commanding generals part, what tactics they use, the quality of the troops they are using, and the raw courage and professional skill they demonstrate. This of course, can also be modified by specific actions that the player characters or enemy champions take.
For example, lets say that the player characters are on Army A's side. If the enemy champions kill or overrun part of the player characters in an important skirmish, it can then be exploited that the the enemy champions apply their skills and magic in such a way as to help their troops in the larger fighting--this then would allow a potential set of modifiers to be added to their side's die roll, or series of die rolls, which would thus potentially influence more casulaties immediately upon the enemy, or some tactical achievement which gains their side some other benefits for the next round in the battle, like permitting a regiment to flank the enemy forces, siezing an important ridge, crossing a river in strength, retaking the gatehouse, whatever really, depending on where the victory occured, and what forces were available on hand to be used in an exploitation operation.
This second kind of scenario, and the mechanics that are used with them, are designed to play through an epic battle with the emphasis on the operational and heroic aspects of the battle, and the forces involved, rather than hyper-focusing on what each and every unit of 1000 troops does or fails to do. This is also designed to be played quickly, in a dramatic manner that encourages the scope and sweep of an epic battle, rather than getting bogged down in endless rules and minute details.
Also for example, using this system, the benefits of having 30% more troops than the opponent can be as easily factored into a series of strategic rounds, just as easily as a series of modifiers for lets say your character leading a crack regiment of 3000 elite human warriors all armed with +3 longswords and wearing +2 Platemail of Fire Resistance, and wearing rings of invisibility and wearing cloaks of Elvenkind.
It is a bit more complicated to try and detail here, but in short, this outline gives you some idea of the two approaches and systems that I use. It also works smoothly and elegantly for the campaign.
Semper Fidelis,
SHARK