(Tested only on Android 2.3+)
Phonegap works perfectly with webstorage.
Appmobi has some conceptual flaws that make it difficult to implement. Basically c2 assets are zipped during appmobi build and then unzipped on first execution inside the app data folder.
This leads to two problems:
1) Your app size is bloated (container + zipped assets + unzipped assets + cache)
2) Application updates pushed via appmobi update system destroy saved data.
I said "pushed via appmobi update system" because currently it's not possible to update a C2 application bundled with appmobi even using the new version number feature and, frankly, looking at the source of their containers I doubt will ever be.