Both the Moodle Assignment Activity and Google Drive can be used to collect, assess, and provide feedback on assignments, however each tool has features that may be better suited for different situations.
If you would like to ....
automate/control when assignment is available, window for submissions, number of submissions allowed
integrate marking with Moodle's Gradebook
have a separate place to accept submissions for each assignment during the semester
If you would like to ...
allow the instructor and/or students to add feedback to a paper or presentation in the actual paper or presentation itself
have students upload large quantities of image, video, or other larger file size multimedia
enable students to work collaboratively on a paper or presentation or spread sheet - entirely online, without having to keep uploading or downloading these documents each time a change is made
accept submissions for multiple assignments in the same place (folder) over the course of an entire semester