It's a gamble; the results can be awesome fun, or a horrible crash-and-burn mess that can't end fast enough.
From past experience, I think I'd try to give some warning hints, if nothing else so that some players don't accidentally make characters that end up nigh-useless (e.g., the techno-whiz hacker PC that ends up dumped in Medieval World, where there are no electronics), while others are awesome (the martial artist cop, who's kung fu works just fine, thanks). So I might warn players that there was some sort of switch going to happen, and promise that I'd try to steer them away from characters that would end up seriously screwed by the switch -- without necessarily outright telling them what the switch would be.
In most fictional stories like this, the protagonists are usually either conveniently qualified for their new homes, or Competent Hero types who are good anywhere (e.g., John Carter was an excellent swordsman and warrior before hitting Mars; our hero in Planet of the Apes was a broadly competent astronaut, not a meek mission specialist). I would try to help the PCs match, or at least make sure they remain about equally useful after the big switch.
I made up a Navy SEAL for a GURPS Special Ops game once, and decided that my PC was an Olympic level swimmer; spent a fair amount of points on it, and figured it would be handy, what with the whole SEa-Air-Land thing. Then we got dumped into a post-apocalyptic desert wasteland, and I was suddenly effectively a dozen points cheaper than everyone else. Whoops. I've also done similar things as a GM, and had it not work out as awesomely as might be hoped.
For example, the GM may find that the PCs end up spending all their time, energy, and effort into fighting (undoing, escaping, or otherwise just not going along with) the switch, which might not be where the GM expects the campaign to go. That can easily lead to a mismatch of expectations, which is often bad for the fun quotient, which is in turn bad for the campaign's prospects.
Changing the PC ("hey, you're a mutant now!") is much the same -- the player might love it, hate it, or somewhere in-between, and how it ends up is pretty random IME. Some players might tend towards one reaction or another, but the reaction can also be affected by other things -- e.g., if the player's had a crappy week, is getting over a cold, just had to unexpectedly repair a house/car/family member, and shows up for game to find the character he made last week has been mutated -- it might be the last straw, even if under other circumstances the player'd be cool with it. So, know your players, and maybe feel 'em out about it beforehand ("Hey, I have an idea that will mess with your PC's status & abilities, but I want it to be a surprise; how would you feel about it?"). Getting some buy-in beforehand is usually helpful, IME.