There are two general groups of fasteners: structural and non-structural. The non-structural designs are those where the part will fail in a mode that is not through the threaded shank portion. Pretty much all external drive fasteners fall into the structual grouping. Virtually all of the low profile (truss, button, oval, flat) head designs in the industrial standards (aerospace excepted because of special head envelopes and requirements) fall into the non- structual group and will break from the underhead radius into the recess at a load lower than the UTS of the threaded portion.
The socket head cap screw design is an exception and it is structural, even under a wedge loading. The common pan head design is semi marginal. In almost all cases it will carry a full thread UTS in both straight and wedge tensile, but there are drive types and fastener sizes where it will not be sound under a wedge loading.
We had a long time engineer in our office who used to say that you can have a low head or a strong head, but not both.
One place to see this effect is in ISO 898-1, where they state in the scope of the spec that "Certain fasteners may not fulfill the tensile or torsional requirements of this part of ISO 898 because of the geometry of the head which reduces the shear area in the head as compared to the stress area in the thread such as countersunk, reased countersunk and cheese heads (see clause 6)."