Actually, you'll hit the limits of DOM-style JSON parsers as soon as your data is larger than about half the available memory, since you'd most likely want to build your own model objects from the JSON, so at some point both of them must be present in memory (unless you're able to incrementally destroy those parts of the DOM that you're done with).
Anyhow, IMO a proper JSON library should offer both, in a layered approach. That is, a lower level SAX-style parser, on top of which a DOM-style API is provided as a convenience.