How do I sync my iPhone app favorites with my desktop favorites...and/or vice versa
to synchronize your Ultimate-Guitar account with the Favorites section of the app you need to complete the following steps:

1. Go to "Home" screen of your UGT app on your device.
2. Go to "Account".
3. "Sign In" with your Ultimate-Guitar.com account.
4. When asked "Do you want to synchronize Favorites with your website account?" choose "OK" (Wait till the process is completed in full).

Note: If you already have favorites on your device, the app will ask you to keep them or not (choose "Keep Tabs" to not lose anything in your Favorites).

The synchronize button will appear in your Favorites section after this procedure. You can use it for further synchronization.
The app did not ask if I wanted to keep them, it just wiped out all my favorites.