How do I compare two columns for equality in SQL Server?

CASE WHEN is the better option

SELECT 
  CASE WHEN COLUMN1 = COLUMN2 
    THEN '1' 
    ELSE '0' 
  END 
  AS MyDesiredResult
FROM Table1
INNER JOIN Table2 ON Table1.PrimaryKey = Table2.ForeignKey

I'd go with the CASE WHEN also.

Depending on what you actually want to do, there may be other options though, like using an outer join or whatever, but that doesn't seem to be what you need in this case.

What's wrong with CASE for this? In order to see the result, you'll need at least a byte, and that's what you get with a single character.

CASE WHEN COLUMN1 = COLUMN2 THEN '1' ELSE '0' END AS MyDesiredResult

should work fine, and for all intents and purposes accomplishes the same thing as using a bit field.

The use of IIF? And it depends on version of SQL Server.

SELECT
IIF(Column1 = Column2, 1, 0) AS MyDesiredResult
FROM Table;