Here's the problem. You're an infantryman hanging out in your barracks, eating some good food (Biology had just been researched), all of a sudden a bunch of guys carrying maces run by. So what do you think?
They're LARPers.
Of course, when they turn and attack you, you're totally fooled. Caught by surprised, you're easily destroyed.
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In the Battle of Guilford Courthouse, American War of Revolution, 1781, the Patriots had three distinct forces. The first line was local militia, North Carolina farmers and tradesmens. They were armed with old style rifles (1745-1760ish vintage). (The first line was expected to fire twice or three times and then bolt for home). The second line was more militia, but they were more experienced--veterans of Cowpens and Kings Mountain, for example, as well as Virginians. They had regular rifles, but not all of them had bayonets, they were expected to fire and attempt to hold, but it was understood that they might not be able to stop the Redcoats ... for the that was the purpose of the third line. These were Continental Army regulars. They had modern rifles with bayonets, and they were battle-seasoned. The plan and its execution was brilliant. The British almost lost the war that day -- until their commanders ordered their artillery to fire into the melee, forcing the Americans to withdraw but at great cost to themselves. While the war would not end for Cornwallis until Yorktown, after this pyrrhic victory the British cause was all but ended.
So why am I recounting this? Because I want to demonstrate that the units in Civ are necessarily vague. You would need three different unit types to represent the American order of battle (four if you included Lighthorse Harry Lee's Cavalry). Now, you can overly complicate the game by including thousands of different units, or you can use older units of equal strength to represent the differing units. In this case, you would have Longbows in the first line (the withdrawing ability makes this nice and accurate), the second line would be Muskets, while the third line would be Riflemen (and experienced ones at that). Now, some might argue that promotions could be used to distinguish, but that doesn't work either because it's really the equipment that's represented by the power of each unit. If you gave the first line Machine Guns, it doesn't matter how inexperienced they are, they're going to do damage. Here's the fun thing: they still may cut and run, even with the machine guns. Not everyone earns the Red Badge of Courage.
eventually british guns did prevail but the thing is chance is an equal to any gun. 
