The advent of ultra-high resolution wall-size displays and their use for complex tasks require a more systematic analysis and deeper understanding of their advantages and drawbacks compared with desktop monitors. While previous work has mostly addressed search, visualization and sense-making tasks, we have designed an abstract classification task that involves explicit data manipulation. Based on our observations of real uses of a wall display, this task represents a large category of applications. We report on a controlled experiment that uses this task to compare physical navigation in front of a wall-size display with virtual navigation using pan-and-zoom on the desktop. Our main finding is a robust interaction effect between display type and task difficulty: while the desktop can be faster than the wall for simple tasks, the wall gains a sizable advantage as the task becomes more difficult. A follow-up study shows that other desktop techniques (overview+detail, lens) do not perform better than pan-and-zoom and are therefore slower than the wall for difficult tasks.