The Miiverse clone is called "Xboxverse". In Japanese, it's called "Hakoverse" (箱バース), with "hako" (箱) meaning "box" and being one of the console's nicknames in Japan. To be clear, this isn't a Microsoft Japan joint, but rather, the work of Japan's fledgling Xbox 360 owners. In Japan, the Xbox 360 hasn't exactly lit the country on fire.
The Xboxverse is browser-based and obviously not part of Xbox Live. Community members, however, are uploading Miiverse-style drawings—as well as drawings that would most likely be clamped down on pretty quick in the Miiverse.
Also I couldnt post pictures of what players drew for the game The Adventures of Tintin due to NSFW content but you know where this is going to..