With MapInfo there is a facility to move labels to a new position. This new position means your label has been personalised but this is still in label format unlike ArcGIS where moving a dynamic label means first changing it to annotation text.
Finally, QGIS can only move labels if you have the X and Y co-ordinate information in your attribute table. With the latest version of QGIS the ABC labeling options include the ability to select the fields in the attribute table which contain the X and Y co-ordinate data. Within Layer labeling settings select Placement then in the Data defined section select the X and Y co-ordinate options. With these options activated you are then able to use the Move and Rotate functionality.