Well Its not really a matter of Number crunching, but here are the number crunches (assuming pop 5.. no Math...Stone Hooked)
Pyramids in Sparta
13 hpt + 3 Forests and a Whip of 2 pop at the end=26 hpt +3*40 + 60
450-180=270/26 hpt
So about 10 turns after the Stone is Hooked up... but you won't be at pop 5 then so rearrange to pop 3...9 hpt...18 with Stone
=15 turns Give or Take
Oracle/Axes in Athens...~10 hpt +7 fpt +20*7
The Forests alone take care of the Oracle, the Axes can come out ~1/3 turns.. plus probably a whip for 60 (clean Axe/Spear) every 2 pop or every 8 turns
So over the ~15 turns the Pyramid is being built. Athens gets about 9 Axes and the Oracle (~4 axes less for SH)
Disadvantage... To rush Engineer, Forge needs to go in Sparta then.
Advantage: the Engineers don't get polluted with Merchants if you put the Colossus in Athens
Alternative #2
Athens at 4
Pyramids
8 hpt +7 Forests +2 Whip =16 hpt+7*40+60=
450-340=110= 7 turns (of course you won't chop that fast, but extra will can be used for axemen.)
Sparta at 2
SH+Oracle=effectively 210 (with Stone)
6 hpt +3 Forests= 6+3*20=
210-60=150 =25... maybe less since you should grow to 3 or 4 then..15 turns if its just the Oracle
Actually I'm thinking the Pyramids are much Better in Sparta, So that Athens can rush out units, which are more easily whipped and Athens had a better Food advantage than production
at pop 3
Athens=+6 f, 5 hammer
Sparta=+4 f, 9 hammer
The other option is to go with the Option 2, Oracle in Sparta, Pyramids in Athens, but use the Pyramids immediately for Police State, Allowing Athens to mass Axes To finish off the Chinese (Axes/Phanxes, a Settler for Marble City.. to speed the Oracle, Workers/Granaries can also be built while waiting for Stone/Priesthood)
I think I prefer that method... you get the Oracle Probably After the Pyramids, guaranteeing the First GP is an Engineer, for Machinery, even without running a Forge.
So Final result: prebuild 1 Axe, 1 Phalanx in Athens, and then whip them out, concentrate on Food bonuses the the Copper, Chop like mad after the Stone, Cow and Wheat are hooked up. Whenever Athens reaches 4, once Working on the Pyramids, add an Axe or Phalanx on top and immediately whip 2 pop for 25 overflow=50 extra hammers
As for the Pre-build in Athens... assume 10 turns till stone is hooked up
during that time
Pop;Fpt;Hpt
3;6;5... 5 turns of this=25 to an Axe
4;4;8...5 turns of this=33 on the Axe+32 on the Phalanx
T1 whip the Axe=28 overflow=56 hammers [pop3]
T2 collect [pop 4]
T3 whip the Phalanx=27 overflow=54 hammers [pop3]
T4
Plus the base production which is 6,8,6,6,=26*2=52... although you should
So you get 56+54+52=162+ to the pyramids in the first 4 turns, no chopping... in another 3 turns you should have a 4 pop... so another 50 hammers +Axe/Phalanx from a whip
Actually Looking At it, it seems like the best 'pre-build' method might be to whip a Worker (once you hit pop 4), rather than prebuilding Axes. Because with all those Forests, and the Food bonuses, Athens is perfect for a Chop the Pyramids then exploit whips to whip ~2 Axeman for 1 pop under Police State.
So I'd say OPTION 1
Athens:
Axe until pop 4 then
1 turn on Worker and whip (for 2 pop)
Return to Axe (prebuild)
[Archer if Stone Not Ready]
Whip Axe to Pyramids when Stone Ready [Chop As Fast as possible]
Let pop climb... Whip Axe->Pyramids whenever pop 4
Sparta:
Axe (while pop Growing to 3 at least)
?Worker?
?Settler?
Oracle
I'd say probably wait on the Settler, don't race Mao, Kill him.
Disadvantage.. Later Oracle.... and Its risky cause Saladin has Marble
OPTION 2
Athens:
Axe/Phalanx Prebuild
[whip 1 Worker at pop 4]
Oracle (as soon as Priesthood)
Granary
Axes/Phalanxes*
Whip Axes into Oracle whenever pop=4
Sparta:
Pyramids... Just start and keep building, chop after Oracle done.
Forge
OK all considered, because the Oracle is one you can most easily lose, get that one first, In Athens. (then a Forge to go with the Pyramids in Sparta so that GP #2 can be an Engineer for Machinery) [25 turns after Oracle=GP, <20 Turns after Forge=GE]
OR 50 turns after Oracle, <10 turns after Forge.... You actually probably want the Prophet first, for Theocracy... Machinery isn't useful until you have Civil Service, unless you want to Bow rush.. so the Forge can be built normally rather than Rushing it in Sparta... it should take ~12 turns