If you are much more advanced than the enemy (eg. you have modern armour for attack, while they only defend with spearmen), then it is definitely much better to have each unit attack individually, since tanks and modern armour have blitz ability (can attack multiple times in one turn). However, if your enemy is equally matched in terms of technology and its Modern Armour vs. Mech. Infantry, there may be the need for an army.
Usually in modern era, if I am thrown up against Mech. Infantry with my Modern Armour, I'll have a few armies of modern armour as it means that when one unit gets down to 1HP, it will retreat and let the next in line attack. Usually, three (four with the Pentagon) is enough to kill one mech. infantry. I'll also use bombers and radar artillery and possibly cruise missiles if I have that many resources to throw around like that to soften them up. However, if the bombers/RA manage to reduce all defenders to 1HP, individual modern armour will be OK to use for a mop-up.
Due to the unpredictable nature of early warfare however, armies are a MUST!!! If you get a GL in ancient times, build an army immediately, combine three regiments of swordsmen (two archers and a spearman if you don't have iron yet). Make sure that you build the Heroic Epic ASAP when your army wins a battle as it will make it much easier to gain Great Leaders, making it possible to build more armies, and to rush wonders.
As age goes on, armies have less and less significance in warfare, unless your enemy is evenly matched. But if you use enough artillery or bombers, you'll only need individual units to mop up (usually) on their cities (bombardment also helps reduce walls to rubble and the population to something less defensible).
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