This actually does very little as far as refactorings go. Lines 276, 279, 283 are essentially the only things that are deduplicated. The rest is still duplicated, just within the function instead of in two separate functions.
The result is that there isn't really much gain. Theoretically, if you wanted to implemented a third field that works similarely to settings/preferences, you couldn't reuse this method. You'd have to walk through it, try to understand what it does, and add the appropriate if statements and so forth. No abstraction was really created.
I personally couldn't understand what the differences were between the two objects based on this, so I refactored it as I went through:
// This object is a good reflection of the key differences between these two objects
// We can then effectively ask ourselves why these differences exist:
var perOrganizationUserDataMapping = {