Actually the compressor design has very little to do with a compressor stall, axial and centrifugal flow designs can both have induced stalls if the operation of the engine gets out of tolerance. In fact most axial flow compressors actually flow their air onto a final stage which is a centrifugal compressor face that directs the compressed air through a scroll into the combustor housing. To visualize this simply imagine an axial flow compressor drum that is attached to the front of the centrifugal compressor impeller, the 2 compliment each other very well. These are known as a compound compressor design.

In general centrifugal compressors are less efficient than their axial flow siblings, but they are much simpler to design, produce and maintain. Axial flow compressors make more sense when the engine is being installed in an aircraft because the designs can retain a much smaller engine diameter, which lend themselves to fitting into aircraft fuselages. Another point to consider is that of maximum CFM flow, axial designs have multiple stages that can ingest and compress huge volumes of air while still retaining a modest inlet diameter. To get the same performance from a centrifugal compressor the design would have to be increased in overall size and diameter which presents the aircraft designers with weight and fit issues when installing them into an airframe.

When discussing stalls in a turbine engine we are not actually talking about a stall that is aerodynamic in nature, like that that of a wing. In the context of this discussion the term stall simply means that the internal air pressure rises beyond limits in the aft section of the engine and when it reaches the aft end of the compressor it attempts to impart a limiting force, essentially it is acting as a brake and acts upon the spinning compressor as such. Since the compressor is turning at a very high speed and carries a huge amount of inertia the effects tend to be non-linear resulting in a violent pulsation that can cause all of the things I described above.

The word stall has many meanings but I think this is the most accurate with regard to this discussion:

v. stalled, stall·ing, stalls
To halt the motion or progress of; bring to a standstill.

It is entirely possible for aerodynamics to induce compressor stalls. In the case of supersonic aircraft the jet inlet design is crucial for proper operation and prevention of compressor stalls.

In the end it's ALL about controlling airflow with a very high degree of precision.