I think building a shrine is WAY more important than building a monument. A shrine gets you a pantheon, which can significantly boost the value of tiles in your main cities, or other benefits. Also gives you a shot at getting a good religion. Add on some of the beliefs you may get and the shrine is a future source of food or happiness. A monument just gives you culture. Nice. But not decisive. A shrine can give you a real edge. I only build monuments before shrines now if I have a hammer happy start that lets me get the monument out before pottery, or maybe a turn after. Generally, when I research pottery, I interrupt whatever I was building to rush the shrine. Getting it a few turns earlier may make the difference of a pantheon now, with good choices, or one way late where the best choices are already gone.