Both of them express act of a lot of sound. But I think that noisy is using about people,machines, and places that annoy you. And loud is using about sounds,voices, or music.

Arash's answer made me think. Here are some more thoughts: (1) Something can be noisy without being loud. For example, if you walked into a room of 20 people and they were all talking at once, but in low voices, you might say it's noisy, but not loud. (2) Arash is right in that if you say something is noisy, it often implies you find it annoying. Things are noisy if there's no "cuteness factor." For instance, a box full of mewoing kittens could be noisy, but not annoying (if you like cats!). Oh, and the noun counterpart of the adjective "loud" is "loudness." It is used less commonly.