Based on more recent info that's been spreading around... The story as we know it is:
There's some mimiga named Su, she knows there's an outside and wants to see it. She doesn't seem to have any relevance aside from that arc from what I gather.
There's a soap named Puu, he's a jerk and eats mimiga, you need to stop him.
Curly had almost no relevance in the story itself whatsoever aside from being there to drive things forward, as far as I can tell. We don't even know if the professor is a character since there's no screenshots or info that really confirm this whatsoever, it could just be a scrapped idea that pixel drew for one of those ending screenshot ideas. But I have a suspicion he eventually became Itoh.
The locations a tad later in the game, assuming
grasstown the thicket and sand zone are in the same order as they are in the final game, are what had the better storytelling parts, so this would be around the balcony where the game
It's starting to look like Pixel didn't exactly scrap as much from the beta as we thought, but rather just redid the earlier sections of the game and cleaned up the later sections, because the stuff in the later sections of the beta seem to resemble content that exists in the final game more and more. The only part of the content that was cut that truly matters is the frog kingdom because that was actually a full on story segment that was probably replaced by the Labyrinth, which I guess I don't mind,
Monster X is hands down the coolest fucking design in the entire game so I say it's a fair trade.
Areas sprawled out more and it just seems that what little story was there was alot more shallow than what the final game had.
tl;dr : The beta was alot more Cave than Story