Personally, I would say NAND-to-Tetris is a (great) freely available learning resource for people looking to actively learn more about computers and digital logic from the ground up. It is mostly structured like a course you would take and the game it leads up to is a means to an end.
Turing complete on the other hand is a more playful approach that guides you through the individual steps (though it still requires you to look up quite a lot of things on your own) with a little story and provides more smaller challenges instead of just one big end goal. In addition to that, it features a relatively powerful sandbox that allows you to interact with things and there's a scoring system for complexity and runtime for all your little solutions that gives it a small competitive side.
I wouldn't say one is better than the other. NAND-to-Tetris is a learning resource with a game in it and Turing Complete is a game with learning resources and a sandbox in it.
To which I would add, TC is more newbie friendly, what with the cartoonish GUI, while Nand2tetris expects that you're already more technically adept and capable of working at the level of command-line.