Feedback activity is available in Moodle core whereas the Questionnaire plugin is a contributed one.
Although similar in nature, the plugin have some basic differences like:
* You can use the Questionnaire plugin to encourage the students to complete a questionnaire. You may choose to award the student a grade upon completion. Whereas the feedback activity is not graded.
* Questionnaire allows to Save and resume the answers. This feature allows the users to leave the questionnaire unfinished and resume from the saved point at a later time.
* Questionnaire also allows to create branching questions. This feature allows you to create Yes/No and Radio type questions to have child questions depending on the students choice.
* The other difference is the question types supported
Via Miloš Bajčetić