or is it as if both worlds have been stitched back together as if they're a single planet?
This - though there tend to be 'rough edges', usually prone to tectonic activity, severe or rapidly changing weather conditions, electromagnetic interference and other localized problems. They're 'bad spots' for all sorts of reasons, and the effects are inconsistent - it might be fine for a few hours, and you can gaily stroll back and forth and have a picnic. But then, all of a sudden it might become hideous skin-flaying hail and lightning storms. Or the grue turns up and starts chasing you around and stealing your sandwiches.
Visually, there'd probably be like a heat-haze effect in the air. You can see what's there, and it almost seems to blend in, but it looks a bit like a mirage or as if there's a lot of heat rising from the ground.
I'm not sure how random the overlaps would be - whether you'd start finding alternate-world shopping malls in the middle of the Atacama Desert, or an oil tanker in the middle of the Great Plains, but the idea is that the two worlds are fused together, and that there's a certain element of collapse and decay to things, and a definite element of otherworldly strangeness. Almost post-apocalyptic, but without the complete collapse of civilization that one would expect in such a setting.
My main points in having the two worlds together are:
A) Familiarity, so we can experience places we know exist as players, but have them be changed and altered
B) Exploration, so we can also explore new and unusual places, but possess current cultural references and technology while doing so
C) Introduce new creatures, technology and peoples to a familiar world, without abandoning or removing ourselves too far from what we know.
tl;dr, I like pop culture jokes/references, modern cities, and M16's, but I also like aliens, ancient hi-tech civilizations and giant robots. I wanted all of them in one thing.