The one without the barcode is the limited CoroCoro Comic version which was distributed on October 15, 1996. The one with the barcode is the regular retail version which was released on October 10, 1999, almost 3 full years later.
Here’s another fun fact, which always struck me as funny as a Westerner. Pocket Monsters: Pikachu (aka Pokémon Yellow or Special Pikachu Edition in the West) had its retail release in Japan on September 12, 1998, a full 393 days before the commercial retail release of Pocket Monsters: Blue on October 10, 1999.
Everything is the same inside the box. The only tiny difference is the back of the box missing a barcode for the Coro Coro version. Some grading companies make the distinction on the label and call it the mail order or the CoroCoro version.
As for rarity. I don’t have the exact numbers either way. But if we take the Masaki cards as an example, we know Japanese kids who were avid fans of the Pokémon franchise loved to mail in to receive merchandise so I wouldn’t be surprised if there’s more CoroCoro versions than regular retail versions. Because most kids probably already had the game after those 2 mail in waves.
I believe the vast majority of Japanese Blue copies were distributed through the CoroCoro offer, so the retail stamped version is actually more scarce as the CoroCoro release was available for 3 years before it hit the retail shelf. At least that’s what I’ve read from multiple sources. As far as price differences, there seems to be none established (yet) between the two different prints.