When using the main inbox search you are able to use keywords to filter data. When not in the main inbox search keywords are not supported (See screenshot)
In this small search box you are unable to use the same keywords and only supports text only. On top of that the filters under Last activity does not include Assignee which the only work around to filter by who the case owner is to filter the entire view for one user which creates endless amounts of users based views which is not ideal to set up.