$id_active = 1;
$id_swap = 2;

UPDATE article_test
// the column to update is 'sort_id' and since it is also the column I need to test,  then I use the same value for CASE right?
SET sort_id = CASE sort_id
WHEN $id_active THEN $id_swap  // sort_id 1 to become sort_id 2
WHEN $id_swap THEN $id_active // sort_id 2 to become sort_id 1
WHERE sort_id IN ($id_swap,$id_active) // test only rows with sort_id 1 & sort_id 2

UPDATE article_test
SET sort_id =
  CASE
    WHEN sort_id = $id_active THEN $id_swap
    WHEN sort_id = $id_swap THEN $id_active
    ELSE sort_id
  END
WHERE sort_id IN ($id_swap, $id_active)

CASE sort_id
  WHEN $id_active THEN $id_swap
  WHEN $id_swap   THEN $id_active
  ELSE sort_id
END

CASE
  WHEN sort_id = $id_active THEN $id_swap
  WHEN sort_id = $id_swap   THEN $id_active
  WHEN sort_id LIKE '' THEN blah
  ELSE sort_id
END

UPDATE article_test
SET sort_id = CASE sort_id
WHEN $id_active THEN $id_swap
WHEN $id_swap THEN $id_active
else sort_id end
....