The Si is politically more powerful as a member of the Dark a council. Save for intervention by the Emperor, The Si is effectively the chief executive of his sphere of influence. The Wrath does not serve as an executive. He instead acts as a watchdog at the Emperor's behest. He doesn't control any aspect of Imperial life. The Wrath is outside of the normal imperial chain of command and is not over the Dark Council. His authority only extends over the Dark Council when the Emperor himself gives him that authority
As the Head of Ancient Knowledge, I don't see the SI having that much pull over what goes on in terms of Imperial direction. They'd probably preoccupy him (or her) with digging through tombs or something.