George Zucas said:
radius since there are more materials remaining than the other
Stress relief at a sharp corner can be accomplished by either adding material, or removing material, as seen in both of your pictures.
From what I remember,
From the first picture, an adequate fillet radius may leave not as much flat surface area for stress flow between mating parts, and there would be concentration of stress where the parts meet. An undercut can provide a larger fillet radius with a greater flat mating surface, and thus less stress concentration at both the corner and where the parts meet.
Threaded connections can have an undercut, with no loss in strength as long as the undercut is not below the thread root.
Gear teeth can have an undercut at the root, thus lowering stress concentration there also.
Type of material - a ductile material can experience some plastic flow, and so can get by with a smaller radius at a corner. A brittle cannot.
Internal properties of the material itself, such as Inclusions, can be instigators of internal cracks occurring before that at a fillet. Fillet radius and type may not be all that critical.
To stop a noticed crack from advancing from a corner of say a flat plate, one can remove ( surprising ! ) material, by drilling a hole at the base of the crack. The new larger radius of the hole becomes a stress reliever.