Just tested my game with the XDK Crosswalk export and the save game worked just fine as far as I could tell.
I have a save point at the start of every level so the player can continue where they left off if they exit the game.
I like CocoonJS better because it locks the screen and scales nicely. XDK Crosswalk does not lock screen orientation right now so it looks unprofessional. But at least the save works. Crosswalk is pretty new so hopefully it won't be long before they fix the screen lock.