One could do worse than quote OED:
Etymology: Alteration of new adj., apparently originally in order to give an eyecatching appearance to the written form of commercial names.
Although it always follows that etymology and basic meaning, OED has three definitions:
1. orig. U.S. In commercial use, forming the names and designations of products and companies.
1892 U.S. Trademark 22, 189 (U.S. Patent Office) 20 Dec. 1 Nuform... Trade-Mark for boots, shoes, slippers, rubbers, sandals, and analogous foot-wear.
2. a. Chiefly Brit. Forming the names of types of popular (esp. dance) music which revive earlier styles, typically incorporating more modern elements, as nu-disco, nu-energy, nu house, nu-soul, etc. See also nu skool adj. and n.
1991 Washington Post 25 Oct. (Weekend section) 21/2 The Nu Skool Jam tour..also features Australian pop/rockers the Newsboys.
2. b. nu metal n. a style of rock music characterized by staccato guitar riffs and typically combining elements of hip-hop (esp. in vocal delivery) with heavy metal and industrial music.
[1991 Washington City Paper 6 Sept. 38/4 Heavy metal ripped off punk's sound and forged the ‘new metal’ known as thrash.]
1995 Herald (Glasgow) (Nexis) 17 June 10 The earnest guitar-crunching trio squeeze out an overly-polite nu-metal racket.
It doesn't differ from neo- much, other than in register. Commercially, Nuform chose nu- because of its similarity to new. Similarly with nu-disco, nu metal and the like: those who coined the terms (presumably in the music industry/“scene” before the newspapers) chose nu- because of its similarity with new. In both cases, neo- would not have worked so well, as it generally requires a Greek root to combine with and it’s unlikely that the target market would appreciate it.