Ok. Some quick clarifications. Armies suck badly in vanilla Civ3. End of story. Use them on defense only really.
Even in C3C, it's still a toss up IMO. If there are specific army abilities you want to utilize, then build an army. However, my general rule is that if you are using a "fast attack" unit that could normally attack twice in a round (movement permitting), you are wasting your offensive capability by putting those units in an army.
Sure. An army of MA gets 4 attacks per round. Um... That same army would get 8 attacks if they were just 4 separate MA units.
If you use Artillery tactics in combat, you'll find that you have about zero need for offensive armies. I would much rather build an army of MI, stick a stack of artillery on it, and then use MA to destroy whole stacks of enemy units at a time. The AI will almost always put its units in big stacks, especially later in the game when it's got railroads built (it's not something the AI plans, it just happens due to movement rules). Sure. You could use an army to attack a stack and get an assured single kill. Heck. Maybe even a few kills. But if you use artilery to reduce all the units in the stack to 1hp, then you can attack twice with each fast unit into the stack, killing 2 units per MA. The only issue is when the last unit attacks you'll take the square. You can either time it so you attack with an MA with movement left over so it can retreat back into your starting square, or advance and move some extra MIs and whatnot into the space to move forward for next turn's attacks.
I have very rarely lost an MA using this tactic. Maybe one out of 100 fights, even when attacking MI. The same tactics apply when using calvary, although cannon aren't as effective as artilery, so there's some argument left for using armies for punch factor. I really really don't see much of any use for armies offensively in the modern age though. They are much better used defensively to hold positions (and protect your stacks of artilery).
But that's just how I do it...