Tetris 2 on Famicom and Tetris 2 on NES are pretty different. The Famicom Tetris 2 plays like an actual Tetris game and includes 2-player, battery back-up saves, and an extra game called Bombliss. Also Koichi Sugiyama composed the music (the composer for the Dragon Quest/Warrior games). The Tetris 2 North America and Europe knows is actually called Tetris Flash in Japan and is like the weird love child of Tetris and Dr. Mario. While it too has a 2-player mode, it lacks a save feature, bonus game, and at least to me, is no where near as fun/easy to pick up as regular Tetris. While still on the topic of Tetris on NES, the Famicom version of Tetris is different from the licensed NES version being developed by Bullet-Proof Software rather than Nintendo R&D1.
Other games that are different on other consoles that come to mind are: Sonic Unleashed on PS3 vs PS2, Sonic Generations on PS3 vs 3DS, Sonic Colors on Wii vs DS, Ghostbusters II on NES vs GB, TMNT on GBA vs every other platform it was released on, The Adventures of Batman & Robin on SNES vs Genesis vs Sega CD, Mighty Morphin Power Rangers on SNES vs Genesis vs Game Gear vs Game Boy, Mighty Morphin Power Rangers: The Movie on SNES vs Genesis, and Strider on NES vs Genesis.