Triggers - How Do You Join INSERTED Vs DELETED Tables?

I want to compare the before and after values of an UPDATEd column using a trigger. I want to know if the value in the column has changed. Simple? No!

As you know, SqlServer puts the before image of the UPDATEd rows into the DELETED virtual table and the after image of the UPDATEd rows in the INSERTED virtual table.

So you would get the before and after data by doing a SELECT on these tables.
But here is the problem - how do you join the tables? What if there are >1 rows in these 2 tables (because the UPDATE affected >1 rows) - how do i know which "old"/DELETED rows correspond to which "new"/INSERTED?"
Ok - I could join the 2 tables on the primary key, but what if the primary key was updated? In that case the join would not work - the DELETED table would contain the old primary key value and the INSERTED table would contain the new (different) primary key value. In fact, ALL of the columns may have been changed by the UPDATE.

Now, there is another thing to try with triggers - the
IF UPDATE ( <columname> )
test. This is designed to tell you if a specified column was UPDATEd by the last UPDATE. However, this will return TRUE for any UPDATE that mentions the column - even if the UPDATE does not change any data! So I cannot determine whether a certain column has had its value changed with this either.

So then you can try another test mentioned in the docs for CREATE TRIGGER - the
IF COLUMNS_UPDATED()
test. However, this will report that a column has been updated, NOT whether the data has changed as aresult of that UPDATE.
So if you UPDATE the value in the column to the same value as it was beforehand (admittedly, a pointless thing to do, but it could happen in some apps), this fuction will say, yes, this column was updated.

So my question remains - how do I know if the data has changed in a column after an UPDATE, using a trigger?
Any ideas?