Which compressor is more like to surge and stall - axial or centrifugal?
Axial for sure.  Its blades are wings subject to aerodynamic stall within the blade array. 

Centrifugal compressors just throw air outward; they don't really "stall" if in-flow is restricted, but will surge due to the pressure drop and resulting load reduction on the compressor.  Centrifugal compressor surge is what is happening when you block a vacuum cleaner and it goes vwwwwwweeeeeeeeeeeeeeeeeeeeee.

Axial compressors, being an array of little spinning wings, depend on a controlled angle of attack on the blades and are much more sensitive to flow disruptions.  And once they do stall, the surge and flow disruptions throughout the engine are more severe (those whomp whomp sounds and flames coming out the front of the engine as reverse pressure waves are induced, that sort of thing).

So if you want efficiency and high compression ratios, you go with axial and live with the sensitivity, the high cost and complexity.  If you want insensitivity to inflow disturbances and can live with a larger diameter engine and less efficiency, and want to make the engine cheaper, you go with centrifugal.