It appears that mousemove wins, at least when I implement the following code:
Code:
Private Sub EitherListview_MouseMove(ByVal sender As Object, ByVal e As System.Windows.Forms.MouseEventArgs) Handles lstFrom.MouseMove, lstTo.MouseMove

        Dim itmClick As Windows.Forms.ListViewItem

        'make sure the left mouse button is clicked
        'and that we have a listview to work with
        If e.Button = Windows.Forms.MouseButtons.Left Then
            If TypeOf sender Is Windows.Forms.ListView Then
                With CType(sender, Windows.Forms.ListView)

                    'get the node here
                    itmClick = .GetItemAt(e.X, e.Y)
                    If Not itmClick Is Nothing Then

                        'allow a drag drop of this node
                        .DoDragDrop(itmClick, DragDropEffects.All)

                    End If

                End With
            End If
        End If

    End Sub
When this code is in effect, the double click event for the handled listview never gets raised. Does anybody know why?