The AVL tree is used for sorting when there is a custom comparison function because we cannot guarantee that the user-provided comparison function conforms to the requirements of the underlying standard library sort functions. Websites have a habit of providing nonsense comparison functions (e.g., using function() { return 0.5 - Math.random(); } to "shuffle" via sorting) and we need to ensure that these sorts will give terminate.

EDIT: Sparse mode is when JSC::JSArray switches from storing the array data as a vector to storing it in a map. You can see from the code at http://trac.webkit.org/browser/trunk/Source/JavaScriptCore/r... that a vector will be used for sufficiently small arrays (< 10,000 elements) and for larger arrays that are at least 12.5% full.