I don’t understand why Judas’ betrayal of Jesus is so important. Peter also betrayed Jesus by denying him three times. Was his betrayal less harmful than Judas'?

Practically, the Temple leaders could have found and arrested Jesus when he was out in public but, as Scripture says, they feared the crowds who might riot upon such an act (e.g. Matt 21:46). To find Jesus at a more private moment would surely have required more “inside knowledge,” which Judas could provide.

Theologically, no one could lay a hand on Jesus until his “hour” had come. He was always able, until he freely chose to lay down his life, to evade their attempts at arrest (e.g. Jn 8:20). This may also have caused the Temple leaders to conclude they needed inside information.

And while God could have allowed another way for Jesus to be turned over, Judas fulfills Scripture, which says: Even my close friend, who ate my bread, has turned against me (Ps. 41:9).

Betrayal and denial are fundamentally different. Through betrayal Judas handed Jesus over. Denial, while surely sinful, is to deny association with Jesus, and does not amount to handing him over. Thus it is less harmful to Jesus than what Judas did.