Short answer: yes and no (EDITED as per comments below)
There are fundamental differences and trade-offs. XML is a markup language, particularly suitable for textual documents (xhtml, docbook, various kinds of office docs).
And good enough for many other tasks. Problems mostly arise for it having hierarchic model (instead of, relational as in SQL, or object-graph as in oo languages).
JSON is an object notation, meaning it has bit more natural fit for handling data-oriented use cases; cases where xml sort of works, but where there is more cost in overcoming impedance between object and hierarchic models.
JSON is not a perfect fit -- it's still data, not objects (no identity, can't do full graphs) -- but it is more natural than XML.
And as such, it is easier to build tools to do good decent and simple data binding.
So: there's plenty room for both, and I would expect both to be used for long time to come.
Not always in optimal way, but both can do plenty of use cases well enough.
For what it is worth, since writing my original answer, I have seen JSON absolutely annihilate XML for data-oriented/data-interchange use cases for companies I have worked for. SOAP (etc) will start significantly shrinking, and "plain old JSON" data interchange (esp. with RESTish frameworks, JAX-RS for Java for example) will take over.
And yet XML is much better for textual markup.
