I don't think either notifies you about the background transfers, but e.g. Operas default cache limit for Application Cache is ~50 MB according to http://www.opera.com/support/usingopera/operaini/.

Sorry for nitpicking, but I think local storage is a part of Web Storage (http://dev.w3.org/html5/webstorage/), and not Application Cache (http://www.whatwg.org/specs/web-apps/current-work/multipage/... or http://dev.w3.org/html5/spec/offline.html).

I think that the Application Cache quota is not strictly connected to the local storage and session storage limits.

That's correct. Chromium has talked about unifying all these kinds of storage under one quota system, but it's not done yet.