There is a tradeoff going for GEs. Since getting a GE as your 1st or 2nd generated great person (as opposed to the Meritocracy freebie) sets the GP costs up a level, you set subsequent great artists back a bit. So the GE comes at the expense of, very roughly, half a landmark during most of the game. So that early GE is probably costing you 1200 or so potential culture.
And then what are you going to spend it on if you are trying to get the earliest win? Building something that give you no culture, but more GE points is a loser as you further delay GAs. Building the Sistine is ok, but looking at my last game (1675 AD deity win), Sistine got me about 2275 in extra culture. That probably is worth the delay in GA production, but in the end, Sistine only shaves off 3-4 turns from the win.
And then there's the possibility of saving it for Cristo. In that case, you probably have to keep the GE around for 100 turns (so gold cost), which indirectly affects other stuff. If you happen to shave of 10 turns from build time, however, you probably save 25% on 2 semi-expensive policies (say roughly 1600 and 1800, for a total culture savings of 850 culture). That minimal savings is also a reasonable argument against generating 2 GEs (using the 1st on Sistine and the 2nd on Cristo). A 20 turn Cristo build feels really, really painful, but it's not quite as brutal as it seems in terms of culture cost.
And then what are you going to spend it on if you are trying to get the earliest win? Building something that give you no culture, but more GE points is a loser as you further delay GAs. Building the Sistine is ok, but looking at my last game (1675 AD deity win), Sistine got me about 2275 in extra culture. That probably is worth the delay in GA production, but in the end, Sistine only shaves off 3-4 turns from the win.
And then there's the possibility of saving it for Cristo. In that case, you probably have to keep the GE around for 100 turns (so gold cost), which indirectly affects other stuff. If you happen to shave of 10 turns from build time, however, you probably save 25% on 2 semi-expensive policies (say roughly 1600 and 1800, for a total culture savings of 850 culture). That minimal savings is also a reasonable argument against generating 2 GEs (using the 1st on Sistine and the 2nd on Cristo). A 20 turn Cristo build feels really, really painful, but it's not quite as brutal as it seems in terms of culture cost.