It was a genuine enquiry, as it happens.
So, in essence, it is "how good it looks" for any given person for any given image, and is not a property of the sensor.
In which case, it does seem a spurious addition to the vocabulary
In Sigmology, "pixel sharpness" has an objective meaning it will take just a moment to explain. According to Foveon catechism, we first remember that 'output' pixels - squares on the computer screen - do not correspond directly to the photo sites on the camera's sensor, at least with the Bayer system. One 'output' pixel - say it's wet-earth brown - is a computational result using data from the red+blue+two green photo sites spread out side-by-side to form one Bayer set, and adjusted according to the values of farther-flung adjacent sites. With the X3, the output pixel is also computed from the red, green and blue sensor data. But with X3, the sensor elements are stacked at one location that corresponds exactly with the output pixel's location. This makes a real difference where you have a sharp edge between tones or colors. Rather than a zone several interpolated pixels wide, ranging from white to black through shades of grey, the X3 image jumps from a white pixel to a black pixel, hence sharpness at the pixel level or 'pixel sharpness.' Viewing X3 files above 100%, you can see this on the monitor. Having a sharp lens and not having an AA filter also helps. Did I get this right? There is a paper on the web by Rudolph J. Guttosch called "Investigation of Color Aliasing of High Spatial Frequencies and Edges for Bayer-Pattern Sensors and Foveon X3(R) Direct Image Sensors," that demonstrates this experimentally. It's easy to imagine how this effect could be diminished at the higher pixel density of the new sensors. At the shockingly low 4.7 mp of the nearly equal-sized old sensor, it's delightfully evident, says someone who bought his DP2x last month! Sorry if this was pedantic; as a new convert, I have the mysteries fresh in my mind.