"The content between Yakuza 3 US/UK and Yakuza JP is a little different in that we took out certain bits in order to bring the game to the west in the time alloted for us to do so," a Sega rep told IGN. "The parts we ended up taking out were parts that we felt wouldn't make sense (like a Japanese history quiz game) or wouldn't resonate as much (such as the concept of a hostess club)."
You may have gone on a karaoke date with Rina in the demo. In the original game, you meet her in a hostess club, and have to buy her gifts and learn about her in conversations. Now, we suppose, she'll just randomly call you like she did in the demo. Somehow, the dating won't be affected, as the Sega rep assured IGN that "the story experience was the same as the Japanese version."
Who can blame Sega for cutting some of the more culturally Japanese elements from this role-playing game about modern Japanese culture? After all, it must have been in a rush to release on the same day as Final Fantasy XIII.