Problem
Even though Jira integration sync shows as completed when checking the sync status, there is an error of Invalid value: Two values with same label (xxxxxx) but different IDs found in your project. Please update one of the duplicate values in Jira before attempting another sync.
This is only an issue when a Jira field has 2 or more values with the same name.
Solution
In Jira, editing the value name to be unique from any other value in that specific field is the expected fix.
Please note that if the assignee field is triggering this error, the full name and public name need to be changed.