Thank you for your question regarding this text (John 8:3-11). It is one that is difficult to answer as you have phrased it because two different things are in view. It is almost as if you were to ask "Which is more important, a faithful wife or obedient children?" Let me explain what I mean.
In regard to the casting of stones, Jesus didn't throw a stone because he wasn't qualified to do so. He is citing the Mosaic requirement that the first stones be cast by the witnesses to the sin/crime. Jesus wasn't there at the event, so he would have violated the law of God if he had cast a stone. His challenge is to the accusers, because the witnesses also must not be complicit in the crime/sin. (The situation reeked of a "set up"—that two men could have actually seen the adultery and yet that the guilty man escaped.) Jesus' challenge was the requirement of the law that a pure witness must cast the first stone; someone involved or falsely accusing would have been liable for the same penalty they were seeking to have imposed on someone else. This was a warning to them.
In regard to his warning to the woman, Jesus wasn't declaring her innocent of wrong doing. There was no legal case now pending, but that didn't excuse her from the Judgment Seat of God where she would be called to stand. It is a call to repentance, but phrased more broadly than simply a reference to this one area of sin.
So, I cannot say one is more important than the other. Both display the pure justice and wisdom of God, and a large measure of mercy.
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