At this point, it sounds like IndexedDB will be more highly adopted then WebSQL.
Mark West did a nice overview. I summarized a his comparison slides below:
• A real, relational db implementation on the client (SQLite)
• Data can be highly structured, and JOIN enables quick, ad-hoc access
• Big conceptual overhead (SQL)
• Sits between full-on SQL and unstructured key-value pairs in “localStorage”
• Asynchronous, with moderately granular locking
• Joining normalized data is a completely manual process
Code Comparisons: http://hacks.mozilla.org/2010/06/comparing-indexeddb-and-webdatabase/.