Comparison of the Axial-Flow and Radial-Flow Compressors
Axial-Flow compressors do not significantly change the direction of the flow stream, thus Axial-Flow Compressor allows for multiple stages.  Radial-Flow Compressors can not be staged.
While the Radial-Flow Compressor has a larger Compressor Pressure Ratio (CPR) per stage, the multi-stages of the Axial-Flow compressor allows for a larger overall CPR.
The frontal area for a given air flow rate is smaller for an Axial-Flow Compressor than for a Radial-Flow Compressor.
The Axial-Flow Compressor has a higher efficiency.
Disadvantages are the higher cost to manufacture the Axial-Flow Compressor, and the Radial-flow Compressor is more durable than the Axial-Flow Compressor.