SQL Server 2008 – Calculate Average Between Two Dates of Different Rows

You don't need 30 join conditions for a FULL OUTER JOIN here.

You can just Full Outer Join on the PK, preserve rows with at least one difference with WHERE EXISTS (SELECT A.* EXCEPT SELECT B.*) and use CROSS APPLY (SELECT A.* UNION ALL SELECT B.*) to unpivot out both sides of the JOINed rows into individual rows.

WITH TableA(Col1, Col2, Col3) 
     AS (SELECT 'Dog',1,1     UNION ALL 
         SELECT 'Cat',27,86   UNION ALL 
         SELECT 'Cat',128,92), 
     TableB(Col1, Col2, Col3) 
     AS (SELECT 'Dog',1,1     UNION ALL 
         SELECT 'Cat',27,105  UNION ALL 
         SELECT 'Lizard',83,NULL) 
SELECT CA.*
FROM   TableA A 
       FULL OUTER JOIN TableB B 
         ON A.Col1 = B.Col1 
            AND A.Col2 = B.Col2 
/*Unpivot the joined rows*/
CROSS APPLY (SELECT 'TableA' AS what, A.* UNION ALL
             SELECT 'TableB' AS what, B.*) AS CA     
/*Exclude identical rows*/
WHERE  EXISTS (SELECT A.* 
               EXCEPT 
               SELECT B.*) 
/*Discard NULL extended row*/
AND CA.Col1 IS NOT NULL      
ORDER BY CA.Col1, CA.Col2

Gives

what   Col1   Col2        Col3
------ ------ ----------- -----------
TableA Cat    27          86
TableB Cat    27          105
TableA Cat    128         92
TableB Lizard 83          NULL

Or a version dealing with the moved goalposts.

SELECT DISTINCT CA.*
FROM   TableA A 
       FULL OUTER JOIN TableB B 
         ON EXISTS (SELECT A.*  INTERSECT  SELECT B.*) 
CROSS APPLY (SELECT 'TableA' AS what, A.* UNION ALL
             SELECT 'TableB' AS what, B.*) AS CA     
WHERE NOT EXISTS (SELECT A.*  INTERSECT  SELECT B.*) 
AND CA.Col1 IS NOT NULL
ORDER BY CA.Col1, CA.Col2  

For tables with many columns it can still be difficult to identify the specific column(s) that differ. For that you can potentially use the below.

(though just on relatively small tables as otherwise this method likely won't have adequate performance)

SELECT t1.primary_key,
       y1.c,
       y1.v,
       y2.v
FROM   t1
       JOIN t2
         ON t1.primary_key = t2.primary_key
       CROSS APPLY (SELECT t1.*
                    FOR xml path('row'), elements xsinil, type) x1(x)
       CROSS APPLY (SELECT t2.*
                    FOR xml path('row'), elements xsinil, type) x2(x)
       CROSS APPLY (SELECT n.n.value('local-name(.)', 'sysname'),
                           n.n.value('.', 'nvarchar(max)')
                    FROM   x1.x.nodes('row/*') AS n(n)) y1(c, v)
       CROSS APPLY (SELECT n.n.value('local-name(.)', 'sysname'),
                           n.n.value('.', 'nvarchar(max)')
                    FROM   x2.x.nodes('row/*') AS n(n)) y2(c, v)
WHERE  y1.c = y2.c
       AND EXISTS(SELECT y1.v
                  EXCEPT
                  SELECT y2.v) 

The transaction log does not not contain statements, it contains the physical changes occurred in the database. If you see a log record that indicate a delete you cannot know if this was a DELETE statement, a MERGE statement or a wide (split) UPDATE statement. If you see an operation indicating an INSERT you cannot know if it was an INSERT (...) VALUES (...) or it was an INSERT (...) SELECT (...) or it was an INSERT (...) EXEC or it was a MERGE or it was a wide (split) UPDATE. And so on and so forth. Specifically, the transaction log does not intend to substitute for an audit trace.

The transcriptional replication agent has means to reconstruct T-SQL operation with identical effect as those that changed a published article, but how it does it is not public information.

If you want to monitor data changes, use Change Tracking or Change Data Capture. If you want to monitor T-SQL activity, use profiler traces.