The circumstances were indeed different. Regardless, I have a reputation to uphold. What will the German Confederation think of Austria if it cannot project power for the benefit of the German states? If I sit back and do nothing, the German states are going to be quick to assume Austria is not fit to lead the Confederation, and much less a united Germany.

Point is: I have a reason to be involved in this.

EDIT: And if we're going to talk about real-life, I should point out that Sweden didn't intervene on behalf of Denmark. They stayed out of the conflict.