Simplicity vs information
Burn down charts are simple. A single line racing towards zero as the project is completed. Anyone can understand this chart, and it does not need an explanation. However it can hide important information, for example the effects of scope change.
Scope change is when work is added to or removed from a project. We are all familiar with scope change, the client suddenly demands extra features, or work is removed from a project to meet a deadline. A burndown chart does not show this information as clearly as a burn up chart.
A burn up tracks completed work and total work with two separate lines, unlike a burn down chart which combines them into a single line. The total work line communicates important information - is the project not yet complete because work is slow to be done, or too much new work is being added. This information can be crucial in diagnosing and rectifying problems with a project.
Presenting project progress on a regular basis
If you are presenting project progress to the same audience on a regular basis, for example weekly customer progress meetings, you are probably better off with a burn up. It will allow you to easily show them you are making progress, even if they have been adding more work, or testing has revealed problems that are adding work to the project.
Convincing customers to stabilize project scope
Scope creep is the enemy of every software project. In the face of scope creep burn down charts start to look like little progress is being made. However a burn up clearly makes the scope creep problem visible to the customer. This may even help you to convince them to stop requesting changes and allow the project to complete.
Fixed scope projects
There are certain limited circumstances in which a project may have a well defined fixed scope. If a project is guaranteed to have fixed scope, the burn up chart communicates no more information than a burndown chart, so the simplicity of the burn down chart is preferable.