I am not sure what these widgets are called, but they are the ones used to assigned tags to questions on SE and appear in webmail apps such as GMail and Hotmail as well:

If someone could chime in and tell me what they are called, that would be great, but I will call them "List autocomplete" for now.
When using these widgets, there are 2 implementations of "delete", that is when a user presses the backspace key.
On SE, the behaviour is to turn the previous item into a text field, and allow the user to change the text of that tag. We can also click on a previous tag and edit it (the 1, 2 are steps to go through when the backspace key is pressed):

The other behaviour is to select the previous tag the first time backspace is pressed. The second time it is pressed, the whole tag is deleted. Editing a previous tag is not possible (the 1, 2, 3 are steps to go through when the backspace key is pressed):

Which approach is better? Have any of you done any testing to determine whether users will prefer to modify the previous item or get rid of it completely? What do users expect when using these type of widgets? Any studies/testing data would be nice to have too.