It's a difficult one without a little bit of information:
Like where was the alternate spawned? Whats the differences? Are they just climate or are the people and their lifestyles different?
For instance the supposed link to our ancestory roots of apelike creatures walking through the plains might have been the point for an alternative to be sculptured.
Perhaps one drank some water with a protezoa that eventually caused some form of ailment that created a change to humanity as a virus, or a change in evolution.
Perhaps there was never slavery, and the populous was allowed to bloom, where instead of warring internally they managed to move to trade and bartering (Of course this would shift the whole worlds destined path)
Perhaps a climate change, the equator moves, the poles move and Africa becomes a frozen tundra. It's animal population have then evolved to survive the cold (the elephants look like wooly mammoths and Hairy Rhino's)
Perhaps Africa is the only continent left intact after a comet hits.
So the next question is how do your characters (hero's and villians) fit into this world? what are their plans? and during their plans what random actions could occur to complex their plans?
Are they just trying to escape? are they trying to find something that is lost or hidden? are they searching for a person or alien?
I as all these questions and mention these points as they are of use, because afterall your characters might be sucked through some interdimensional portal from a more advanced world.
Or they could awake in a post apocolyptic environment after a solar flare bombarded the planet and changed peoples superpositioning on a quantum level.
I'm sure you can think of something more imaginative
