The task definition key is tightly coupled to the process definition the task belongs to, i.e. it always references the activity id in that process definition (guaranteed by Javadoc in Task#getTaskDefinitionKey). Migration should therefore update that key.
Impact: If a task is migrated to another activity id, the task form cannot be resolved after migration and there is no API to correct that. In tasklist, the task can only be completed by using a generic form.
Updating the task definition key is also required to resolve task listeners correctly.