I don't remember scores, but I'm pretty sure I've gotten to level 16 before. I'm not sure it's possible to get any further, the blocks kind of start to fall instantly at that point. I guess you'd need some luck with the pieces and also how the stack is shaped when it starts happening.
I love Tetris on the NES The official NES version; I never had the chance to try the Tengen version. I also have played the Game Boy Color version, which is neat, but at the time I wasn't into it, so I gave my copy to my sister I should buy another copy someday, since I still carry my GBA SP with me.
Sorry if I don't agree that THAT ought to be the factor that disqualifies the NES version. I've never in my life played a Gameboy game multiplayer. You need two consoles, two carts and that little cable. Forget it.
Tetris was always super-easy to get multiplayer going on Gameboy, though. Because that game was bundled with the system, literally EVERYONE had it. And I always carried the Link Cable in my backpack, so it was never a big deal to get a head-to-head game (or two, or three) started.
You never even got to play Pokémon multiplayer? That was the go-to multiplayer game for me and my buddies in college for years.