You simply can't play Dredd if you don't keep the helmet on for the whole film. It's a central part of the character. There's even one story where it's revealed Dredd has special dispensation to keep his helmet on in the presence of the Chief Judge. All other Judges must remove their helmets, but not him.
Stallone tried too hard. He bellows, "I am the Law!" during his trial. When Urban whispers it while talking over the PA, it comes across as part threat, part statement of fact.
They also nailed Dredd's extremely dry, pitch black sense of humour. For example when he, Anderson and the perp they've captured are in the elevator,
Anderson, "Sir...he's thinking about making a grab for your weapon!"
Dredd, "Yeah".
Anderson, "...now he's changed his mind".
Dredd, "Yeah".
