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Pixel scrapped the 2003 beta because it wasn't fun according to him. Can you imagine a version of Cave Story with no weapon xp where everything had limited ammo and the only way to get ammo was to buy it? The shop system was a ball and chain around the entire game.
The 2002 beta could've been remedied with a melee weapon or infinite ammo.
Though, it still is a beta, incomplete. I can understand how that shopping system would be annoying in Cave Story, it's also rather bothersome in Kero Blaster, and it really encourages farming;
HOWEVER, Kero Blaster doesn't have ammo limitations, whereas Cave Story Beta had you buying weapons constantly so you wouldn't run out of ammo, pitting you into an endless cycle (and often screwing you over with bosses and other more difficult areas)
The beta encouraged exploration much more than the final though, but was extremely lackluster in terms of variety all around (There were about 4 common enemies, and those would get tiring very fast) , thus the final was more linear than the beta, having the player go from one place to another, whereas the beta was somewhat linear, still had more backtracking and unlocking new areas, which probably made the beta feel much larger as well.
What we have right now is a very well polished game, and I think pixel was right to restart development.
Though I still think it'd be nice if he released the beta, but with Tyrone's grasp on it, that's not gonna happen unless we show what the community will do to make it into something really enjoyable.
There are countless beta remakes on the forums, and a really good one in development as well.