I think the single biggest difference would be the degree to which religion would control life.
The surviving popular religious traditions assume a diety that is not overtly involved in the day to day affairs of creation, and is at most looking in and subtly nudging things behind the scenes. Religious traditions with this belief tend to emphasis perfection of secular living over religious ritual. That is, for the most part, religious ritual is confined to certain holy days and often only portions of them.
But historically, this isn't the only sort of religious practice that has flourished. The alternate view, that supernatural things are occuring all the time, also has held sway. As science succeeds in giving natural explanations to most things that we observe, religions that are incompatible with the idea of a subtle and mysterious supernatural world tend to fall by the way side. As a practical matter, I think they also fall by the wayside by demanding too much sacrifice on the part of their practicioner compared to religious practices that demand less departure from mundane matters to tend to the sacred. The classic example would I think be Rome's triumph over the Etruscans.
But with the possible example of folk Hinduism, you'd be hard pressed to find a widely practiced Etruscan style religion in the modern world.
However, in a fantasy world, supernatural things actually would be occuring all the time, the gods are (at the very least through clerics) actively manifesting there power in far from subtle ways all the time, the gods have fairly sizable control over their spheres and apparantly the will to use it, and almost certainly the successful cultural practice would be paying attention to the gods all the time in hourly rituals of propituation, celebration, and worship.
A person crossing from the average D&D world to medieval Europe would I think be struck by how limited of a role religion played in daily life, the economy, culture, and the government. The visitor from the D&D world would be completely familiar with the monastic rituals of unceasing prayer, but would be struck how confined these rituals were to a particular class of people and by the fact that only a single diety would need to be propitiated for the whole of society. The visitor from the D&D world would be completely at home with the notion of every trade having a patron saint, but would be shocked at how little of a role worship of that saint played in the every day practice of the craft. The visitor would be used to every aspect of the craft having a religious role and meaning, and that everything would have the ritual formalism of a Japanese tea ceremony (Shintoism incidently, being a relatively ritualized religion which perhaps in antiquity had something of what I'm describing) where as everything he'd witness would seem so pragmatic, unadorned, and casual by comparison. The visitor from the D&D world would be perfectly at home with clergy being great lords, but perhaps uncomfortable with the idea that head of the mason guild wasn't the high priest of the God of Masons, the Mayor the high priest of the God of Cities or Trade or something similar, and average streetsweepers not noviates at the temple of something.
I think pretty much everyone would be engaged in mutliple religious observances round the clock. The Moslems daily reutine of prayers would pale in comparison to such proper homage to a half dozen deities reutinely, and any number of other dieties as their spheres of influence crossed your path.
I think our visitor might ultimately be struck by how free we are to excercise our lives without the continual meddlesome intervention of some god or the other, and just how little reutine smiting for failing to offer this sacrifice or the other seemed to occur. Battles would be reutinely decided by tactics on the field, not by which side had accidently trod across this sacred field or the other without offering a proper tribute. Peoples lives would be largely theres to live as they wanted without fear that they'd get caught up in a dispute between the Goddess of Love and the Goddess of Marriage that would consume their lives and make a mockery of their choices.
This seems like a whole 'nuther aspect that that will determine the role of religion/gods in a setting. I mean that primarily in this regard: do the gods control what the afterlife will be?
