Dear Michael,
when syncing between iPhone and iPad it is important to activate "Sync System Files" in the Dropbox setting to make sure that sort order and other settings are synchronized, too. - Duplicates are very unusual, though.
To correct that I would suggest the following procedure
- Just to be safe: back up both iPhone and IPad in iTunes
On the iPad (which I assume has all up to date info)
- make sure that "Sync System Files" is on. If it is not and you need to turn in on, sync after doing so; this will export a .plist sidecar file for each document
On the iPhone:
- turn off Dropbox sync
- delete all books and notes from the iPhone (BUT ONLY IF YOU HAVE ALL YOUR INFO ON DROPBOX)
- turn on Dropbox sync
- make sure that "Sync System Files" is active
- select "Reset Sync History"
- sync from the top level book
This will import all books and notes from Dropbox.
I hope that helps.
Best,
Alfons