This comparison is the follow-up to GPT-5.6 Luna vs Claude Fable 5. Each side of that page now has a successor in Vizify, and both successors keep what their predecessors had in common: Paid-tier access and text-plus-image input. Fable 5 and GPT-5.6 Luna are still available, so moving is a choice rather than a migration.
Reasoning control is where they part. Claude Fable 5.1 keeps the five-step range Fable 5 had, from off to extra high. GPT-6 Luna carries the six-step GPT range, adding max above extra high. Both default to medium, and both let you turn reasoning off entirely for a request.
GPT-6 Luna also has two properties Fable 5.1 does not. It comes with a Fast variant at twice the per-token credit rate, and the Vizify app profile names it as the model behind the code-artifact generator for HTML and React output. That second point is about configuration: if your chat model is Fable 5.1 and the Agent calls the code generator, that one step runs on GPT-6 Luna. It says nothing about which model writes better code.