If you don't want to watch the video, a version of this talk was also given at Strange Loop, the slides for that one are available online: http://www.infoq.com/presentations/Functional-Data-Structure...
AMT's are one of clojure's most heavily used container types.
This technique of increasing the node size in order to speed up traversals on conventional architectures is actually quite general. You could do the same thing to finger-trees for example. One disadvantage is that lots of different versions of the same structure take up more space than they would otherwise.
An advantage of applying tree-broadening to a finger-tree rather than a generic balanced tree structure, is that, depending on the ordering, it may make in order traversal faster, because elements that are near each other in the structure are also (in some sense) close together in memory.