Eagle Warrior (Aztec) - 32 = 35-3. I would really love this unit if it wasn't so expensive to build. At the end of the day, that is the difference between it and most of the units on the list now. I play on deity. Hard building 3 to 4 eagle warriors at the start of the game is a bear, even if you have ideal production in your first city. IF you have a neighbor very close, it might work out wonderfully (assuming they are not Sumeria or Nubia, in which case you might be screwed. Sorry but you just won't be able to pump out enough eagle warriors before you get overwhelmed by war carts or Nubian archers, both of which are stronger units.) Yes, the free builders are amazing, but it you are dead or seriously behind a snowballing AI, they just won't do enough. Great unit, but the high build cost is its kryptonite.
Hetairoi (Macedon/Alexander) – 23
Legion (Rome) – 8
Mamluk (Arabia) - 34
Pítati Archer (Nubia) - 47 =46 + 1. It's only real competition is the war cart. Both have 30 strength and enhanced movement. Both relatively cheap. The only difference is the archer can hide in a city or encampment and kill the war cart from there. Thus I give the nod to the archer.
War Cart (Sumerian) - 42