I do have a small collection of setting images we could sift through, it's a little old but I think the link should work, if you wanted to poke around:

[url=http://s29.photobucket.com/user/Genkai001/library/Settings]link[/url]

Fantasy World:

It would be cool if somehow potions and runes could do something together. I think we can do without wands, maybe they're just voice activated or maybe use someone's engery/chi so it could hint a little at whatever the Sci-fi World is doing? I would assume any runes found would generally have one of four images? Fire, water, air and/or rock? 

Sci-fi World:

I think it could be possible to have both sleek and gritty come into play. 

I think we'd have to figure out what tech we'd want and what we wouldn't. In terms of what I could do without: robots. I think robotic technology would be useful but for a robot with human knowledge would be too much for me. And it might be superfluous. I do like the idea of say hover boards, perhaps light teleportation in the works, laser tech within reason, etc.

Modern World:

That would be good, to have people back in the day (era up in air?) communicating with the other worlds and maybe the Modern world severs ties with the other two (which could be in longer communication with one another, probably creating some kind of prejudice against the modern folk?) which is why the modern world became so slow with developing advances in either magic or science?

Misc:

Oh, I meant the mirrors allowed anyone to transport and when the big disagreement happened, the fragments lost the power to bring people to the world but allowed people to somehow leave it? Like maybe a one way connection? So maybe one world has a purple colored mirror and the others have a blue or pink? That would only be needed if we wanted the mirrors to work slightly different though, if we still assume that broken, they work one way and that shards can't be mixed up to form someone else's mirror if pieces are missing. Or something. >_>

I think a prophecy warning the worlds to stay together is probably the most simple route we can take and I'm happy with it.

If it got mixed up (on accident or perhaps someone intended it to?) we could give the Modern world a slip up and have it imply that they need to break away from the other two? Hence when arguments began? If we gave the Fantasy world some kind of darker meaning, that could be rather fun which could in turn make the people start to focus more on their magic? Maybe the Sci-fi is the only one that got it right and is trying to act as mediator while wondering if they should bother fixing the broken pact between the three?