Changing the Apple/iCloud ID will not change anything on the device except iCloud-based data. By that, I mean the data you would see if you signed the iCoud ID onto iCloud.com on a computer. Notes, Contacts, Messages, Mail, etc. You can also see what iCloud-based data you have set up for a particular ID on a particular device by going to Settings>iCloud to see which items are turned on.
With the exception of Contacts, which will allow you to keep whatever is on the device and Merge it to the new iCloud account, any other iCoud-based info will go away.
Not sure what you specifically mean by application data. If you literally mean data that is associated with a particular app (like game data), then that would go away also.
With Family Sharing, however, you will be able to use the info from the original Apple/iCloud ID to set up "Family" Photos, a "Family" Calendar, etc. so would be able to retain that info via the shared methodology.
Cheers,
GB