XML really is a pretty horrible way to represent structured data, but unfortunately it gets (ab)used quite a lot by a lot of developers and websites. So if you're only working with your own stuff, then by all means, stick to JSON and save yourself the hassle. But you still need to learn XML for those times when you end up having to interoperate with someone using an XML interface.
XML is used for more than just AJAX. For example, if you are doing any web services you will definitely encounter XML. Reading/writing configuration files? XML is often used there too.
My advice, however, is to learn enough about it to know when it is a good fit for any projects you might come across, and then do a deep dive when you actually have some work to perform using XML. If you learn it and then wait a long time before applying that knowledge then you will likely be forced to relearn it later anyway.
Let's put the technical (overhead, etc) differences aside for a moment.
JSON is not always appropriate, nor does every client you deal with will want to transmit data to/from you via JSON. XML has its place and IMHO is still the preferred method of sharing data between different companies and platforms.
If for no other reason, learn XML because that's what may bring home the bacon.
One pretty good reason for learning XML is the APIs. If your application is dependent on various external APIs then you are bound to use the output they provide, which most of the time are XML files in return (for example, MediaWiki, OpenStreetMap..etc). In such situations having some basic knowledge of the XML and its structure helps you save the day.
I don't have any experience with JSON, but I do want to add in my two cents about XML. First of all, making the statement that "XML" is easy to learn is quite a leap in my opinion. If by easy to "learn" you mean being able to understand the concept of XML elements and attributes and syntax rules, then sure. If by XML you are including most of the related technologies which actually make XML useful, such as DTD, namespaces, XPath, XSLT, XSL-FO, XQuery, etc., then I'm not so sure that it is "easy". I'm still trying to wrap my head around XSLT well enough to be able to start implementing it in my own work.
That aside, I definitely think that any web developer who wants to stay competitive and useful to the market needs to know XML proper and should be at least familiar with the related specifications.