If I had to choose, I'd say the Nintendo version, whose sights and sounds I definitely prefer. There is also the nostalgia factor that gives it the edge since it was THE Tetris I played as a child. Conversely, my sentimental attachment more than likely is obscuring a more sound judgment. Multiplaying gives Tengen's Tetris an added dimension, and as T2KFreeker said:
Indeed. The physical cartridge itself is beautiful, even if the game's graphics seem a bit lackluster to me. The rarity of the Tengen version also adds a mystique to the game. Whenever I pop it into the NES I feel all warm inside.
Returning to the joy that is multi-player Tetis, let me highly recommend Tetris Battle Gaiden for the Super Famicom. The game is brilliant fun! I snatched a copy off of ebay for like $5 plus shipping, which delighted me to no end. Here is a video to show you what the game is about.