Burndown tracks volume
Burndown is effective when work units are comparable and a sprint backlog is stable. It makes changes in throughput visible.
Hills track confidence
A hill chart does not claim that all scopes are equal units. It makes it clear where discovery, ambiguity, and decisions are affecting progress.
Choose the conversation
Use burndown for capacity and sprint flow. Use Hillchart for shaped work where the central management question is what has been figured out.