it has some effect in all versions (edit: i mean even vanilla and warlords, not just BtS events), but nothing earthshattering. the "game era" is what has the effect, which isn't necessarily the era you're personally in. the game era is the average of the era each civ is individually in. so you can get the splashscreen for classical but if everybody else is in ancient, the game era isn't classical yet.
the effect isn't huge from what i can tell. war weariness gets higher, but not a ton, i think the major reason why it's more painful in late-game wars is that your cities are so much bigger. after a certain era you get two free units when you culture flip a city instead of just one. that sort of thing.
when the game enters a later era, the barbs get some of the old-era techs for cheaper or free. i don't know whether real civs start getting a discount on the old-era techs in addition to the discount they already get from other civs knowing those techs. being in the later era by itself doesn't make techs more expensive, but the later era techs have higher base beaker costs.
, but in a scenario or mod ( like the Earth 1000 BC vanilla scenario ) it can make a diference.
) ......will be corrected ASAP.
