XML also doesn't suffer the problems of a limited set of pre-defined types that JSON has. Its type system is extensible through schemas.
Yes, it is, though there are a variety of schema schemes that can be used with XML.
> It was designed to be extensible through schemas.
It was designed to be extensible through custom tags (in fact, all tags are custom tags); it can be optionally be restricted through the use of schemas, not extended.
> XML also doesn't suffer the problems of a limited set of pre-defined types that JSON has.
Yes, it does, with an even smaller number of types. (Strings, with a couple different representations.)
> Its type system is extensible through schemas.
No, it isn't. Its structure can be constrained through schemas (XML Schema, Relax NG, etc.), which can provide a means of modeling a different type system on top of the data structure supported by XML, but that isn't really "extending" XMLs type system any more than using a Haskell compiler to generate x86 machine code is "extending" the type system of x86 machine code; its just providing a completely separate type system on a different layer.
Also, no matter how you view this, its not a distinction between XML and JSON, since you can do the same thing with JSON, and just as there are a variety of different schema standards that do this for XML, there are a variety that do the same thing for JSON.
XML has become the go-to schemaless format between languages, despite being verbose and having problems with typing. JSON aims to be a general-purpose successor to XML here.