I think this will be a useful community wiki reference: excluding device settings, what iOS user data (the kind of data that is created and stored over time) can only be migrated to a new device through the use of iCloud/iTunes Backup and Restore from Backup?
This can be relevant to anyone buying a new iPhone or other device to replace an old one — if you decide to set the new device up as a "New iPhone", even though you had data on an old iPhone Backup, you will immediately start creating two streams of data that cannot be merged without using 3rd party tools.
This contrasts with data that can be re-downloaded to a new phone after logging in with an Apple ID (iTunes app/music/video purchases, iCloud Mail/Contacts/Calendars/Drive), as well as data that can be migrated piecemeal using iTunes (app documents).
Best Answer
Apple Watch Data
As this support article indicates, the only way to pair an Apple Watch with a new phone and maintain continuity of your data is to restore the new phone from a backup.