Well MM, we do more or less exactly that in my setting, though in a complicated way, and it's been running about ten years or so.
Here is the set-up:
In our world, the human world, there is no magic, but there are miracles.
In the other world, the world of elves (though they aren't called that) and so forth, there are no miracles but there is magic.
Then it gets kinda tricky.
Magic in the other world is extremely dangerous, especially at higher levels and causes all kinds of side-effects. (Like let's say nuclear based technologies that are not properly contained.) Yet most rely upon it to some degree or another and want it to continue that way. Religion in the other world is very simplified and there are no clerics. Many have a belief in God, but no real concept of the idea of a relationship to God.
However the other world has discovered our world and has come into contact with two things. Divine magic in the form of miracles (Thaumaturgy) and the idea of a personal God (through contact with Christians, Jews, and Muslims). Now the leader (a priest-king, though they have a different concept of a priest) of the most powerful Elven kingdom on that world (based in the capital of Samarkand) desires to convert and become a Christian (he already has secretly), really, really liking the idea of a personal God, but even more controversially (to his own people and subjects, not to mention his allies and enemies) he wants to replace what he considers to be extremely dangerous arcane magic with Divine magic as the source of power for his kingdom. Now many in that world are both directly and indirectly opposed to anything regarding either human religion or the idea of replacing arcane magic with thaumaturgy and miracle working. They consider arcane magic dangerous but far more reliable than the idea of miracles from God. Then again you have a radical group within that world that is coming to the idea that arcane magic is destroying nature and the world and that it must be replaced. Some are looking to the idea of what we would call science and technology (though more like magical or arcane science), some to the idea of God and miracles, some to both. So you have a lot of political intrigue, as well as social and sometimes racial intrigue (the giants, a character race in that setting, are good at building and want arcane magic gone, the Eladarin despise the idea of anything human and are very pro-magic even though it often causes disruptions in nature - they are also very pro-nature) regarding magic, what it is doing to the world, and what to do about it. At the same time you have pro-human and pro-human religious elements and groups, and anti-human and anti-human religious groups. And all that all of that entails.
On our world (and the setting is Constantinople circa 800 AD) there is no magic and arcane matters are considered either outright evil or suspect at best. However some in our world have discovered that the other world exists because our world has been invaded from time to time by creatures and monsters escaping from that world to ours. Following these invasions have been earthquakes, and plagues and various troubles. So there are people in our world who distrust and dislike anything dealing with the other world and consider creatures of it to be Satanic or demonic, or at the very least dangerous and untrustworthy. (Many of the monsters that have escaped that world into ours are mutated, for lack of a better word, creatures that were misshapen or twisted by exposure to powerful magics.) On the other hand many on our world, like the emperor and the Patriarch of Constantinople consider this other world to be a source of potential rescue and a possible agency of God (and of the End of Time), and some believe the Eleven Priest King of this other world to be none other than Prester John. At the same time some creatures from the other world have come to our world and are seeking to subvert it by teaching those willing how to practice and master arcane forces. But arcane magic has some of the same bad side effects here as it does on their world (powerful magics for instance tend to kill any animals caught nearby or exposed to it), and indeed that is the hope of those coming to our world to subvert it. Because they wish to kill off any contact between the two worlds and discourage human ideas about a personal God from infiltrating their world.
So it's kind of a complicated web of conflicts, competing interests, and even alliances between arcane magic and thaumaturgy (miracle working), technology, human society and non-human society, our world and the other world, different religious ideas, different political systems, different races, and how all of these things might work together or seek to destroy each other either to fulfill or try to subvert the will of God, and/or to either improve or corrupt the world and nature. Couple that with the fact that both worlds are twins of each other - they are georghaically identical, but are inhabited by different creatures, plants, and life forms and those who know about the existence of the other cannot possibly think that events going on between the two worlds are just a matter of coincidence and happenstance. This adds another conspiratorial angle, I guess you would say.
I never tell the players whose side I am on, or what outcomes I favor (indeed I can see the various viewpoints of everyone involved, even the poor monsters created by accidental or experimental exposure to uncontrolled magic - the only ones I don't favor are the villains after their own gains) or what moral aspects I want them to pursue. Indeed I created the setting and write the adventures with the express intention of giving them very multi-faceted moral dilemmas which they must settle and decide for themselves. I intentionally make it very hard to know what is right or wrong, and if right is all right or if wrong is all wrong, or if it is not more likely everybody is some right, and everybody is some wrong. But in the end that is for them to decide.
Now I've had players tell me I've created a whole new game, and maybe I have to some extent. I just consider it an unusual and semi-historical, semi-real world, sort of metaphysical D&D setting. It's not a kill things and take their stuff setting, but I see no reason or restriction of why the game can't do this kind of thing.
By the way, one of the best things to come out of 4E to me were character classes that were alien enough to be really completely unlike human character classes. So I've taken a lot of the 4E character class elements and adopted those elements for my non-human character classes.
