Knifegrinder, could you elaborate? Specifically, do you have knowledge relating to the data storage capacities of these tools across multiple platforms, and where that data may be stored?
I can just post my personal experience.
Webstorage object works correctly on my device (Android 2.3.6) with:
Phonegap (Webstorage data saved correctly, saved data keeped even on app updates)
Appmobi (Only software renderer tested, webstorage works but there's a loss of data on app updates using appmobi update service)
CocoonJS (Webstorage works fine on my device, updates seem to work correctly)