The PS1 version isn't so much a sequel as an...alternate but kind of the same game as HM64. They both have the same cast and same mechanics and stuff, but with slight differences. 64 had more house extensions and furniture(I think) and event...things, as well as most of the characters having different roles from BtN, some festival differences, and some other stuff I'm probably forgetting. The two are actually fairly different, and in a way so that I never thought that either was definitely superior, but my experience with HM64 is pretty limited.
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Otherwise they're the same games, same characters, same land layout, etc.