I think that you are talking about what Prospero decides at the very beginning of Act V, Scene 1.
Prospero gives two main reasons for showing mercy to his former enemies. First, he says that it is nobler to show mercy. There is more virtue in that than in taking revenge.
Yet with my nobler reason ’gainst my fury(30)
Do I take part. The rarer action is
In virtue than in vengeance.
The next thing he says is that their attitudes are important too. He says that they feel bad for what they did so he should forgive them.
They being penitent,
The sole drift of my purpose doth extend
Not a frown further.
I think it's likely that Ariel's comments matter because Prospero even asks him what he thinks and doesn't just ignore what Ariel says when he answers the question.