The peak stress produced in the 3-pt flexure fixture is at the specimen mid-point (or point contact) with reduced stress elsewhere. Hence, this analysis (stress localization) is ideal to test for specific isolation of stress on the specimen.
On the other hand, the 4-pt flexure fixture produces peak stresses along an extended region of the specimen surface. Hence, exposing a larger area of the specimen is possible with more potential for defects and flaws to be highlighted.