Without knowing their exact implementation, even theoretical design is tough to do, but I see a few possibilities for How a general(s) V assasin(s) would play out:

Setup 1: Generals are extremely weak, army isn't present from beginning.
Generals focus largely on keeping their hero away from assassin, since he can no head to head fight him, Once general obtains a significant army, the Assassin player will likely reach a point where advancing becomes impossible without a heavy level lead from earlier in the game due to narrowing positions as the assassin moves closer to his opponent's base(More possibility for general to surround and cut of the assassin from escape with mass units). So the assassin will have to bulldoze his/her way through once s/he has obtained enough strength to feel no threat from the creeps. In turn, the General will likely spend most of the game pecking away at towers/etc. with creeps and/or demigod until the assassin can no longer defend effectively.

Setup 2: Stronger General, Army is not present at game start.
Early game general is defensive, trying to prevent assassin from gaining too much ground directly, assassin attempts to gain a early lead via killing the general before the general's army is fully established; beyond this, the gameplay follows much of the same route as setup 1.

Setup 3: Weak demigod(setup 1), Army is present from game start.
This poses some interesting ideas, as the General has a couple options, try to prevent assassin advancement with demigod+units, which is stronger but has a higher chance of major failure. Or he can attempt to defend using only units and attack creeps with the demigod, leaving the assassin an easier path to advancement and the general a better attack option. Guessing here the gameplay later on would focus on the assassin trying to gank the general for a moment, take a tower, rinse/repeat, as the general would be a decently easy target.

Setup 4: Stronger Demigod(Setup 2), Army Present
This seems an unlikely option unless the army sizes are extremely small, in which case the general will probably play out in one of two ways: one, the player simply makes use of the general and units as two half-heroes to push where the assassin is not/weak defend around towers; or two, the General uses the hero to defend as best possible and splits units across all fronts to try to achieve a more globally forward position, taking advantage of the assassin's inability to defend all the locations.

Anyways, my two cents, obviously there's a huge number of unknown factors here, such as what happens to the units when the general dies, how xp/leveling is handled between the classes, and how strong the general is by himself compared to an assassin/creep army.

1. How do you see General-style and Assassin-style Demigods match up in just fights involving the two of them; no other units involved?
Assassin should win

2. How do you see General-style and Assassin-style Demigods match up with equally sized armies?
i would put my money on the assassin because it's higher damage output should be more then the buff an army gets from the general. With a general it should be eassier to create a larger army and that's where it's main power should be

3. a. What are the primary advantages you see to playing a General-style Demigod?
Larger army's and being able to support multiple attacks
3. b. What are the primary disadvantages you see to playing a General-style Demigod?


4. a. What are the primary advantages you see to playing an Assassin-style Demigod?
the pure power of an assassin.
4. b. What are the primary disadvantages you see to playing an Assassin-style Demigod?

i see it more like this

Assassin: (wc3 dota gameplay)
Assassin is its own main attack force and will use other units as support and base defence

General: (more traditional rgp gameplay)
The general will use other units as it's main attack force a will support those units during attacks but isn't that powerfull itself.

5. How would you try to balance the power between General-style and Assassin-style Demigods?
Begining of the game:
Assassins shouldn't be to powerfull in the beginning of the game because then a rush attack will be to easy but they should get allot stronger during the game. With the general it's a question of keeping unit production low enough

Vertigodragon makes some real gd points. theres so many scenarios to consider that i actualy believe the devs started this thread just to make us think of all the incredible potential this game has and hence go pre-order rite away!!
Anyway, here's my 2 cents:

1. How do you see General-style and Assassin-style Demigods match up in just fights involving the two of them; no other units involved?
A hero-killing assassin must win in 1v1's in the open. Else it defeats purpose of having such a class. BUT what if a hero's focus is on crippling enemy hero thru debuffs, rather than direct dmg? Is that an assassin too?

2. How do you see General-style and Assassin-style Demigods match up with equally sized armies?
Asin win, but micro-dependant. Did assasin control his units to dodge 1st nuke? did general micro in a way that took down assassin units fast so they can all focus fire on asin b4 it deals much dmg?
In pure equal scenario i believe assasin shud win since general's would have advantage all across battlefield (better/buffed army), while asin can only create an advantage in the area that he is present. For general to overcome that advantage, he'd need to manipulate scenario until his units outnumber asin's.

3. a. What are the primary advantages you see to playing a General-style Demigod?
Rewards player for good micro.
Coordinate multi-pronged attacks.
Gradually builds up to an overwhelming advantage in army strength, leading to sure win IF can survive till late game

3. b. What are the primary disadvantages you see to playing a General-style Demigod?
Reactive in early game. Takes time to build up steady offense while asin can strike hard anywhere, so usually asin would strike first and u'll have to defend against it (yes,generals' auras will result in strong pushes, but as dota players know thats no good in beginning as u end up fighting near strong enemy def tower with long retreat path) . Prone to ambush.

4. a. What are the primary advantages you see to playing an Assassin-style Demigod?
The joy of hunting down generals .
Potentially able to use stuns&slows to chase/escape.
Has offense initiative - you decide where to take the fight. Use hit&run to whittle down enemy defense

4. b. What are the primary disadvantages you see to playing an Assassin-style Demigod?
Potentially less kills hence gold&xp, since each of general's (buffed) units will be making more kills than your units, across whole map, while ur kills mainly come from urself.
If u cant keep cracking enemy defence, u'll b swarmped under by general's units eventually.
Poor defense against general's map-wide advantage

5. How would you try to balance the power between General-style and Assassin-style Demigods?
Adjust exp&gold gained by creep-creep kills (general's income source) and hero-creep kills (asin income) to balance the rate at which the 2 types increase in power
Allow asins to have better base defense/upgrades. Else late game only thing for asins to do will be just defending base against general's stronger units coming from all sides.

Wow, just yesterday you were promoted to a mod (not here, before anyone yells). In a few weeks you really will rule the world

One of the biggest things in my mind when it comes to balancing assasins vs. generals will be how the armies react to the presence and actions of demigods.

In DotA, armies simply attack whichever enemy is closest to them, UNLESS a hero (aka demigod) specifically targets, or locks onto, their side's hero/demigod for his auto-attacks.  If this is done all troops within a certain range drop what they are doing and attack whoever is focused on their hero.  Note that they don't do this when a one-shot spell or ability is used.  This mechanic facilitates a lot of things;
1.  A skilled "assassin" can position himself in relation to the enemy troops in such a way that he will auto-attack the enemy hero/demigod because it is the closest thing to him, without having to click on that hero/demigod.  By attacking the enemy demigod in this manner, he is not "locking on" the enemy demigod, and therefore the enemy army will not focus fire on him.  The experience is like finding a weak point in an enemy's armor or something, and is a lot of fun to attempt.
2.  A skilled "general" or "assassin" who is playing conservatively for some reason can position himself in relation to the armies and enemy demigod so that his opponent can't use the technique detailed in #1 to get free hits on him.
3.  Melee Assassins will generaly run past the enemy troops by clicking movement only, and not lock onto the enemy demigod until they're in range, so that they aren't targetted by the army as quickly.
     There's really more to the strategies than this, but the point is that this sublte aspect of DotA is what makes the control of your single unit and the PvP in that game so intense; you are calculating many things that are presented in a straightforward manner to you.  Do you think you can take down enemy demigod if he has X troops that will be hitting you for Y time when you try it? Can you bait the enemy demigod into trying to kill you when, based on the army setup at the moment, he can't, and therefore you'll kill him? This kind of thing is like a third of the DotA gameplay experience.  While I know that some major things appear to be different in demigod (like more destroyable objectives and, from what little we've seen so far, no "fog of war" which would make ganking very different), I would hope that this subtle aspect of army behavior would remain the same because it's the name of the game.

An important question then would be, will generals be able to say "attack this unit right now?" I would personally hope for the DotA style of play over that.  To a good player, it's almost like you're controlling them anyway after all  And while I understand the division between "assassins and generals", in DotA you have a "hero killer or pusher" and the reason it works is because the army system lets you blur the lines between the two.  You will see "pushers" killing heroes all the time and while not quite as common, you'll see hero killers helping the troops push the line.
Edit: Since, if a general can order troops to drop what they're doing and attack an enemy demigod, that would then require a much larger difference in the strengths of the two types of character archetypes, and probably be less strategic in the long run than the dota style anyway, even though more is being done by the general.

Finally, someone might have mentioned this already, but the "assassins" in dota tend to be stronger early on in the game, but because they are about killing enemy players, they must kill some during the first half of the game or they'll fall behind in the second half.  DotA pretty much accepted this kind of thing as inevitable and I would expect GPG to consider it as well if they haven't yet since it really only makes sense

Something I realised, The Rook didn't auto attack units unless they were already hitting him...

I think that generals should have much more durability than assassins, but assassins obviously have much higher damage outputs.

This means that in General vs Assassin, an Assassin would win, but a General has a lot more staying power. The Assassin can quickly make an impact on the battlefield, but must then retreat due to damage taken, or some other reason you can throw out there. The general is a lot more subtle, but when he goes somewhere, he stays there. This would work because creeps would come in very quickly spawning waves, so the General has ample opportunity to make the buffs work.

An example would be if a General and Assassin met with equally sized armies. The Assassin would most likely bump off the General without problem, but due to the increased buffs he gives and the time it takes, the Assassin would afterwards be swamped and killed.

Think TML vs Artillery. A TML fires its missile, but then is spent and must take a long time to reload. The artillery fires and does not so much damage, but it fires much faster, and it's got splash.