function calling provides a "hint" in the form of a JSON schema for an LLM to follow. the models are trained to follow provided schemas. If you have really complicated or deeply nested models, they can become less stable at generating schema-conformant JSON.

Structured outputs apply a context-free grammar to the prediction generation so that, for each token generation, only tokens that generate a perfectly conformant JSON schema are considered.

The benefit of doing this is predictability, but there's a trade-off in prediction stability; apparently structured output can constrain the model to generate in a way that takes it off the "happy path" of how it assumes text should be generated.

Happy to link you to some papers I've skimmed on it if you're interested!