Examples:
1 - An outrage against the ruling.
2 - An outrage over the ruling.
It seems that they are almost the same thing to me.
There are at least two distinct uses of outrage.
When outrage refers to an insult or attack, against refers to its subject and over is not used:
- The art exhibit is an outrage against public decency.
- The CIA's methods are an outrage against the Constitution.
- The Twilight series is an outrage against literature.
When outrage refers to the reaction to such an insult or attack (anger, horror, moral indignation, etc.), over or at refers to the cause whereas against refers to the target:
- The workers voiced outrage at the new leave policy.
- The lackluster pitching has stirred outrage against the coaching staff.
- The protesters' outrage against bankers over recently announced performance bonuses reached a fever pitch after the Times article.