I play on standard, small, or tiny maps at Regent. I do most of my fighting in the first three eras, particulary the mideval era. My largest military force does not exceed 200 units. I'm sure the AI builds much bigger armies.
I fight in a structured style-- one large artillary stack with slow offensive and defensive units plus a screen/raiding force of fast offensive units. The stack size is calculated to crush and garrison one city with minimal cost and minimal loss of my units. If the artillary is not redlining city garrisons fast enough, I add more arty. The number of offensive units should be triple the typical enemy city garrisons. I can never get enough defensive units in the stack. I restrict myself to 20 cities since I dislike large empires-- all other cities are razed or disbanded.
At the end of the ancient era I have about 45 units: the stack has 6 to 10 catapults + 4 to 8 miscellaneous offensive units + 3 to 5 misc defensive units. Each city is defended by one spearmen (call it 15 city defenders)-- I rely on a good offense. The screen may be 0-4 horsemen.
At the end of the mideval era, I have about 100 units: ~16 cannon + 1 loaded army + ~20 of a widely varying mix of offensive and defensive units + 3 or more workers maintaining roads. The screen is 4 to 12 knights, cavalry, and musketmen. There is now a steady supply train which will have 2 to 4 fresh units in transit at any time. Each city is defended by 2 musketmen. Captured cities may have lots more to suppress culture flips.
In the industrial age, the military stagnates at 100 units as I focus on building city improvements and workers. The stack is parked somewhere and the screen is increased to about 15 cavalry for border guard/punishment work.
The stack is slow, but the AI cannot do much about it until railroads become common, and then there is the screen to chase down... The AI does terrible things to my supply train though.