The drop down calendar is a format applied directly to the filed object while it is on the layout while in layout mode.
Enter Layout mode.
If you do not see the field on the layout while in layout mode, use the field tool or the field picker to add this new date field to the layout.
While it is selected, use the Inspector's data tab to specify a drop down date.
Return to Browse mode and table view and you'll find that this field now has the same drop down calendar as the other.
(In order to specfiy such formats for fields used in a table view, the field has to be present on the layout. Using the modify button to add/remove fields, adds/removes them from the view, but not the layout.)