If you bring Llorissa Faali to the shrine and let her confess, ghosts will disappear and Aizur-Suur will reward you with Antumbral Shield (worth 17000) "For dealing with ghosts". When she will ask you to kill Llorissa Faali (with no additional reward).

However, If you bring Llorissa Faali to the shrine and kill her immidiatly, ghosts will also disappear and Aizur-Suur  will thank you for that, but will give you no reward at all.

It is completely unreasonable to have such great difference in rewards beecause both cases require equal amount of work from the player, and Aizur-Suur really wants you to murder Llorissa Faali, so it would not make sense for her to reward you in the first case, but not to reward in the second case.