There are a couple of options if you want to use T-SQL and SSIS.
You could compare the key columns on the staging table vs ops table to determine if the row already exists and this way you would know if you need to do an INSERT or UPDATE.
If using SSIS you can use the lookup component. Your source componenet will have something like
SELECT keycol FROM OpsTable.
The lookup component will have a source something like
SELECT keycol FROM StagingTable.
You can use the 'No Match Output' option to get all the rows in
OpsTable not in
If using T-SQL you can use the EXCEPT operator like so
SELECT keycol FROM OpsTable
SELECT keycol FROM StagingTable
If you need to compare all the columns (key columns and non key columns) you can use the HASHBYTES and hash all the non key columns for comparison. Please note that HASHBYTES only accepts (VARCHAR, NVARCHAR, or VARBINARY) so you will have to convert any columns that are DATE or such into VARCHAR.
HASHBYTES('SHA1',col1 + col2 + ISNULL(convert(nvarchar(100),ColDate,109),'')
Hope this helps.
You can get more information on HASHBYTES here and on the EXCEPT operator here.