I worked this out for the Exile map. That is, there are 2 gold mines at each base, and 2 gold mines to be captured in the middle. I assumed War Rank will be earned at a flat rate on both sides (3.33 minutes per WR), and that the Gold team will control the gold mine flags about 3/4 of the time. Both teams will get Currency I immediately, but Gold team will buy all subsequent Currency ranks as soon as they are avaible.
For a 3v3 match, after exactly 30 minutes of this (when War Rank 10 is achieved), Gold Team has generated 22683 gold from gold mines and Currency (with the cost of purchasing currency subtracted). The other team has generated 19965 gold from gold mines and Currency (again, the cost of currency is subtracted).
This is a difference of 2718, or 906 gold per Demigod, after 30 minutes of play.
On 4v4, gold generated is 33244 vs 27220.
This is a difference of 6024, or 1506 gold per Demigod.
edit: considering after a half hour, the difference in the gold acquired from holding the Gold Flag for 3/4 of the time is 1800 per demigod (averages 2g/tic more per demigod, so 2g/tic*30tic/min*30min=1800g), buying Currency past rank I is not worth it.
edit edit: Cuz I know it will be brought up, no, I did not subtract the cost of purchasing Currency too many times in a match. Each rank on a given team is paid for only once.
Currency I is at 6 min 40 sec (WR 3). Currency II is at 13 min 40 sec (WR 5). Currency III is at 20 min (WR 7). Again, per my calculation, it's 3 min 20 sec (200 seconds, or 100 tics of gold mines) per War Rank. War Rank in the game is gained at every 810 War Score on default settings.
On Prison (there is only 1 gold mine flag in the middle), on 3v3, Gold Team gets 18854 total gold (6284.6/Demigod) and the other gets 18688.5 total gold (6229.5). Again, this is based on the assumption Gold Team controls the middle gold mines 3/4 of the time. (This is done by giving Gold Team 3/4 of the gold generated every tic (2g/tic -> 1.5g/tic) and the other team 1/4 of the gold generated (0.5g/tic), hence the fractions.)
edit: Currency I gives 4g/tic to every Demigod. Currency II gives 6g/tic, Currency III gives 8g/tic. This is not cumulative: a new rank of Currency replaces the old rank, it is not in addition to the old rank.