Which is the main advantage of an APU's centrifugal flow compressor?

The main advantage of an Auxiliary Power Unit (APU)'s centrifugal flow compressor is indeed its shorter length compared to an axial compressor. Centrifugal compressors use a different design mechanism, which allows them to be more compact and, therefore, shorter in overall length. This compactness is particularly advantageous in applications like APUs, where space is limited. The centrifugal flow design enables high-pressure ratios in a single stage, which effectively supports the operation of the APU without requiring the additional length that an axial compressor would entail for similar performance characteristics.

While other factors like weight, efficiency, and altitude performance are important considerations, the design and function of centrifugal compressors lend themselves to a more concise form factor that can fit within the restricted spaces often found in aircraft.