I ran the "experiment" described above for 20 turns. The only change was that I upped production so each city would produce 1 unit per turn.
Recall that the three types of units were:
"Warrior" A/D/M = 6/4/1
"Archer" A/D/M = 5/5/1
"Swordsman" A/D/M = 4/6/1
All units were flagged both "offense" and "defense".
I was Roman (north center of map) with Greeks to my southwest and Egyptians to my southeast.
I let the Governor make all "my" build decisions. I also let peace reign for 8 turns before starting simultaneous wars which I waged more aggressively against the Egyptians.
Results:
I. Peacetime builds = first 8 turns (each Civ = 24 units total):
Ia. Romans = 24 Warriors
Ib. Greeks = 6 Warriors, 5 Archers, 13 Swordsmen
Ic. Egyptians = 12 Warriors, 1 Archer, 11 Swordsmen
II. Wartime builds = next 12 turns (each Civ = 36 units total):
Ia. Romans = 36 Warriors
Ib. Greeks = 14 Warriors, 8 Archers, 14 Swordsmen
Ic. Egyptians = 13 Warriors, 7 Archers, 16 Swordsmen
III. Total builds = 20 turns (each Civ = 60 units total):
Ia. Romans = 60 Warriors
( 100% Warriors )
Ib. Greeks = 20 Warriors, 13 Archers, 27 Swordsmen
( ~33% Warriors; ~22% Archers; ~45% Swordsmen )
Ic. Egyptians = 25 Warriors, 8 Archers, 27 Swordsmen
( ~42% Warrirors; ~13% Archers; ~45% Swordsmen )
Lessons, Observations, & Best Guesses
1. Never let your governors do all your building for you

2. Fully "balanced" units (the 5/5/1s) were a minority choice, although the spread narrowed ... significantly? ... in wartime.
3. Romans aside, there was a slight-to-slightly significant peference of 4/6/1s over 6/4/1s.
4. The identical Civ and unit settings for the Greeks and Egyptians, as well as their essentially identical strategic starting positions, indicates (i) that there is some randomness in the choice the AI makes to build units (i.e., the Greeks building nearly twice as many archers as the Egyptians overall -- and 5 times as many during "peacetime") and (ii) there is a slight preference given to defensive over offensive capabilities ...
4. Units flagged as "defensive" by the AI were at times used aggressively for offensive purposes -- i.e., marched a long way from home to attack my cities (sorry, I didn't tally the breakdown of offensive vs. defensive assignments by unit type -- but it hardly seems necessary given the identical proportion of 4/6/1s built by the two AI Civs; of course I'll also be the first to admit that determining a meaningful statistical threshhold is most definitely open to question!)
5. THE AI SHOWED NO INTEREST IN THE VLs WHATSOEVER!!! (i.e., the ones in the center of the board were NEVER occupied, even when I lured the AIs units to them).
Next Step(s)
PLEASE COMMENT ON THESE!!! (i.e., do you think they're meaningful/worthwhile or not) --
1. I'm tempted to rerun the test using "Regicide" rules to see if these initial build proportions change significantly.
2. Run a test with the three types of units being 6/3/1, 5/5/1, 3/6/1.
3. Next run a similar test re: movement factors -- i.e., see what it takes to make a unit with a move of "2" seem equally valuable to a unit with a MF of "1".
4. Determine what units in all these tests are "equivalent" (e.g., produced by the AI +/- ... 10%??)
5. Vary offense/defense flags by unit type; see if this has any effects on the result of step (4).
6. Vary hidden/blitz/ZOC flags ... working out a methodology for that one should be interesting, as in the ancient Chinese curse ("May you live in interesting times.")
7. Vary AI aggressiveness ...
8. Find nice, isolated desert island without internet access to recuperate on ...
Onward & Upward!
-Oz