When talking about designing REST services, JSON seems to clearly win.
The whole software world seems to be biased in favour of JSON it seems,
for this criteria. Although I have read, that in many cases REST
services can use XML instead of JSON. I think, JSON's major use case is
in the use within REST.
REST has nothing to do with either XML or JSON, and the concept of REST
was solidified way before JSON existed. In REST, you receive a request,
which for a long time was usually a web form - that is, content type =
application/x-www-form-urlencoded - and in response you emit a document
which represents some part of the state known to the server. The
document can be text, XML, JSON, or something else.
