I like this scene because it's the first (or second, depending on the production) look you get of what's inside of Claudius's head. The first Claudius is sort of frantically castigating and trying to reason with himself, but too swept up in emotions he can't control, so mad at heaven for not answering him. He does a lot of good things with his hands.
The second is ... the saddest sad boy. But he's a calmer sad boy, less pacing and self-directed fury, more slowly turning over his thoughts. They both like to shout at angels, though. He has good thoughtful pauses and mirthless laughter.