Ordinarily I would agree with you except for what .json is: a JavaScript Object. Or, more correctly, its serialized-to-text form. Parsing it is a matter of invoking an extremely common function built into every JavaScript implementation in every browser, and likely optimized to death.

This is one of those weird cases where, despite obj being a simpler format on paper, it would likely be slower to parse due to having to hand-roll the parser in JavaScript and not use the browser's native built-in parser instead.