1. JSON has an easy way to specify data types. In XML you have to have multiple nested tags. In JSON my document can be:
{"mynumber" : 5, "mylist" : ["one", "two", "three"]}
Simple, neat, and fits on one line.
In XML this has to be
5
one
two
three
Of course, I don't know what you're talking about "JSON doesn't even have a bloody date or time type" when XML doesn't have anything but strings. In order to parse this, I'd have to have code which looks for tags and runs my language's atoi() on the content.
Maybe there are libraries that do this automatically. If there are, the XML community does an excellent job of hiding them from developers; I've worked a fair bit with XML, and haven't found them.
2. Easy interface with popular languages. You can just copy-paste a JSON string into a Javascript / Python app. (Warning: If you do this programmatically, it's going to be a security vulnerability.) Whereas if you want to use XML, you have to jump through a lot of hoops. Especially with Java; AFAIK the Java standard lib only ships a specification for XML parsing. So while the org.w3c.xml namespace is there (or whatever it's called, it's been a while), you have to install some Apache lib called Xerces or Xalan or Xavier (or whatever it's called, it's been a while) in order to have XML support.
This is Java's fault, not XML's; but XML was a shiny cool thing at about the same time Java was, so a lot of peoples' main XML experience (or at least mine) is in Java.
3. Is a subset of many popular languages. A lot of people -- especially web developers -- only know one language. If you know JS, then you know JSON. But XML syntax and semantics is very different from most programming languages, and that's a barrier. (General XML is much different than HTML. In particular, you can always see what HTML "does" by loading it in the browser because everything has default styles; not so with a general XML format, unless you go through the pain of writing a complete style yourself.)