In one sense there is no such thing as either a antumbra or penumbra. Neglecting minor diffraction effects, a point source of light is either visible from a given point or it is not visible from that point.
In order to deal with an extended light source, like the Sun, we need to answer two questions to determine the light level at a point.
First, what fraction of the Sun's surface is visible from the location in question? We are all in the antumbra of Venus or Mercury during a transit of the planet, but few of us would ever notice. The vast majority of the Sun's surface is unblocked during such a transit, and the light level here is only minutely affected.
Secondly, we need to look at the brightness of those visible parts of the light source. A person who sees, say 1% of the Sun's surface at one point leading up to a total eclipse (penumbra) is seeing points close to the limb, and some points not so close. Someone viewing 1% of the Sun's surface during an annular eclipse (antumbra), is seeing points that average closer to the limb. Since points closer to the limb are dimmer (see the image of the Sun in your first illustration), the second person would experience a dimmer light from the 1% value than expected.