What is the best way to compare values of whole tables between many databases?
This may not be exactly what you are looking to do, but you could use the EXCEPT statement to get the rows that are different:

SELECT Column1, Column2 FROM DatabaseName1.dbo.TableName1
EXCEPT
SELECT Column1, Column2 FROM DatabaseName2.dbo.TableName2


If you do it this way though, make sure you also do the opposite EXCEPT so you know the rows that don't exist in the other database's table:

SELECT Column1, Column2 FROM DatabaseName2.dbo.TableName2
EXCEPT
SELECT Column1, Column2 FROM DatabaseName1.dbo.TableName1


Hopefully that helps you a little.