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?
The assassin should win, no matter what. If the assassin player made it to this point, he should basically win in my opinion.
2. How do you see General-style and Assassin-style Demigods match up with equally sized armies?
Ok, let's say we got 2 armies consisting of 200 units (just picture some units). We got the assassin walking in front of his army, charging into the enemy army. Because of the assassin in the army, the general's army is slightly losing, lets say 190 (a) vs 170 (g). The general could use a healing spell, healing his units while the assassin keeps pounding on his troops. Even though the general is still losing troops, he's starting to get to equal numbers again: 140 v 140.
The general now uses a freezing attack, freezing all units that are near the general and his army. The assassins troops are now on the losing side: 80 vs 110.
Knowing that his army is losing, the assassin now rushes forth to kill the general and has succeeded in doing so. Still, his army is still losing, although without their leader, are now equally powered in terms of 1v1. The stand is 50 vs 75.
The assassin quickly uses a couple of strong Area of Effect attacks, slaughtering the army: 30 vs 0.
3. a. What are the primary advantages you see to playing a General-style Demigod?
Crushing my enemy with the help of huge numbers of units that I'm trying to keep alive and support.
3. b. What are the primary disadvantages you see to playing a General-style Demigod?
Most likely missing the WOWZORS effect.
4. a. What are the primary advantages you see to playing an Assassin-style Demigod?
BRAAAAAARGH, ME BIG, ME STRONG! And the RPG and tactics part

4. b. What are the primary disadvantages you see to playing an Assassin-style Demigod?
Both using the assassin and still giving orders to your troops.
5. How would you try to balance the power between General-style and Assassin-style Demigods?
Read the answer of question 2, basically, make it so that the general needs his army to kill the assassin, while the assassin needs to get a chance to kill the general.