Depends on what were talking about here. if we talking about a one on one fight, Dredd's Lawgiver is a very versatile and with both incendiary and explosive rounds it would be hard to imagine Judy taking this one. Now if they get to bring a friend to help, Judy's chances go up quite a bit as Bailiff Petri Hawkin-Byrd is a force all his own. Dredd's Lawgiver, while extremely powerful, wouldnt be the advantage that it was in the first scenario.
If we are talking a battle of words, this is all Judy. As we all know Judy has top tier bants, and while Dredd has been known to talk shit himself, Judy's had far more experience talking, where Dredd doesnt usually spend too much time talking before he lights a motherfucker up. Judy would cut him to shreds.