Join tables ON A ∩ B conditions

Question

I wish to join two (or more) tables based on a set of columns that are present in all tables that take part in the join. In other words I wish to join tables based on the intersection set of columns. However each table has extra columns which are unique to that table.

Example

#: A number
-: NULL

Table A

+------+------+------+
| Col1 | Col2 | ColA |
+------+------+------+
| A    | A    | #    |
| A    | B    | #    |
+------+------+------+

Table B

+------+------+------+
| Col1 | Col2 | ColB |
+------+------+------+
| A    | A    | #    |
| B    | B    | #    |
+------+------+------+

Result

+------+------+------+------+
| Col1 | Col2 | ColA | ColB |
+------+------+------+------+
| A    | A    | #    | #    |
| A    | B    | #    | -    |
| B    | B    | -    | #    |
+------+------+------+------+

I've come up with a solution but the performance is horrid, performance is an issue. I don't want to pollute you with that solution. I'd much rather have a fresh set of eyes on this :)

Looking forward to seeing your solutions. Thank you for your time. It's much appreciated.

UPDATE

Thank you for all the responds. However it seems I didn't explain the problem well enough. (Haven't tested all answers yet)

But note how Table B has a row that's not present in Table A.

Table B
+------+------+------+
| Col1 | Col2 | ColB |
+------+------+------+
| B    | B    | #    |
+------+------+------+

And Table A vice versa.

The solution I've come up with unions all tables together on the intersection set of columns to generate a skeleton.

Skeleton:    
SELECT Col1, Col2 FROM TableA
UNION
SELECT Col1, Col2 FROM TableB

Once I have the skeleton I LEFT OUTER JOIN for each table.

LEFT OUTER JOIN TableA AS a ON a.Col1=skeleton.Col1 AND a.Col2=skeleton.Col2
LEFT OUTER JOIN TableB AS b ON b.Col1=skeleton.Col1 AND b.Col2=skeleton.Col2

So the final query looks like this

SELECT s.*, a.ColA, b.ColB 
FROM 
(
    SELECT Col1, Col2
    FROM TableA
    UNION
    SELECT Col1, Col2
    FROM TableB
) s
LEFT OUTER JOIN TableA a ON a.Col1=s.Col1 AND a.Col2=s.Col2
LEFT OUTER JOIN TableB b ON b.Col1=s.Col1 AND b.Col2=s.Col2

Answer 1

Just the thing for a full outer join:

select  coalesce(a.Col1, b.Col1) as Col1
.       coalesce(a.Col2, b.Col2) as Col2
,       a.ColA
,       b.ColB
from    A a
full outer join
        B b
on      a.Col1 = b.Col1
        and a.COl2 = b.Col2