What questions/criteria should a organization ask, when deciding on whether they should keep documents on the share drive, or move them to the portal?
Governance policies typically define this type of question, which doesn't really answer your question.
My general guideline is if people are accessing it regularly, then it should reside on the portal so it can easily be found, indexed, and worked on in a collaborative method. If it's seldomly used, it should be moved to network storage (and still indexed if desired).
Company retention policies tend to dictate these things.
Here are some of the benefits of having documents in SharePoint portal:
There are many more but these are some of the most important ones.
Here are some broad questions, any yes answer to which would indicate you should store it in SharePoint.
SharePoint is designed to enhance the experience of shared editing and reviewing of documents. With the versioning feature and basic workflows, any heavily edited document should be moved.
A good SharePoint information architecture will be able to add metadata properties and all important context to the storage location of the document. This will greatly enhance it's ability to be found after being stored.
If there is an obvious place where the document fits into the site, the document should be moved there. Again this enhances the documents findability.
SharePoint can recognise security settings of a shared folder, but it is far easier manage this in SharePoint.
Any documents that fail all four of these questions could be left on disk and a SharePoint content source configured to include them in search results