Factors to consider with respect to Local Storage.
Local Storage size limit:
Web storage provides far greater storage capacity (5 MB per origin in Google Chrome,Mozilla Firefox,and Opera; 10 MB per storage area in Internet Explorer;25MB per origin on BlackBerry 10 devices) compared to 4 kB (around 1000 times less space) available to cookies. ( source Wiki)
Local Storage Method.
Web Storage:
Web SQL Database:
Indexed Database:
source: html5rocks, sitepoint
All MOBILE broswers have varying degree of support for above local storage method.
The most widely supported method is Web Storage.
If you would like to store more than the limits mentioned above than you need to use the native (OS) features for storing data. Then PhoneGap is the obvious choice for accessing native features.
Storage Options that exceed the above Local Storage Limits:
1) Sqlite Plugin:
You can use the plugin maintained by brodysoft. link here
2) Native File access:
Need to use cordova file plugins. link here