Early game is all about culture. Even for early war, the policy cards unlocking the 50% faster production for archers and horses are extremely critical. Political Philosophy is also a huge milestone for a game since it unlocks huge production boosts for your empire and unlocks the Ancestral Hall, probably the single most important infrastructure building. You do want a decent amount of science early if you are going for a Horseman rush though. But Faith might be the second most important yield early, if you can get enough of it for Monumentality. Classical Monumentality is just so strong, it's basically impossible to lose if you have enough space to settle and a good classical Monumentality golden age.
After the early game, I think it depends on victory type. Science and Domination Victories are the ones where priority shifts from culture to science the earliest I think. It used to happen after rationalism for Science, but might be earlier now that rationalism has been nerfed (I haven't played much in the last 3 months). Domination victories value Science much more after political philosophy, especially in multi-player. Tech advantage wins wars but in single player, I think the best domination games start so early than all yields become somewhat irrelevant.
Religious Victory obviously doesn't care much about science, and for culture victories, science is less important than culture but not by much, since Printing, Flight and Computers are so important. Diplio victories need production the most, preferably via chops, so either science or culture to boost chop value should be pretty important, but I don't really play much Diplo so I'm not sure.
I don't think Culture is ever that far behind science though, even in the victories where science matters most, and early culture is so much more important than early science, that I voted for culture.