My .02 - I generalize a bit - those of you that know more, feel free to reeducate me on the details. It's been a while since I took a thermo class.
What Jay describes occurs not because of weak instability or strong shear - it happens when (as Simon mentioned) a strong, dry inversion occurs atop a deep boundary layer.
When the boundary layer is sufficiently deep enough to allow surface-based parcels to reach saturation, condense, and accelerate vertically prior to reaching the inversion level (a reason to pay attention to 0-3km CAPE values along with surface-based CINH), strong convective development occurs in the form of an intense Cu tower. If the inversion aloft is very strong, though, the presense of suddenly-warmer air relative to the rising parcel causes the parcel to decelerate, lose all vertical momentum, and dissipate as it gets blown downwind within the dry region of the atmosphere just above the inversion. This creates the visual appearance of a solid surface-based tower getting "sheared off" by winds aloft when neither the degree of shear nor the total amount of instability through the entire depth of the troposphere had any direct influence on its demise... just that darned evil cap.
In terms of instability vs. shear: Supercells occur in high instability/low shear environments; and they occur in low instability/high shear environments. It takes a balance between storm-relative shear and effective instability for supercells to maintain themselves. My preference boils down to one basic thought: With strong instability (given zero CINH) and no shear, there are storms, but no tornadoes. With strong shear and no instability, there are no storms.
For that reason I will always slightly favor stronger instability over strong shear, while respecting the favorable effect of strong shear in certain situations (e.g. cold core setups.) Finding the area where shear/instability is maximized and balanced is key; indices such as the energy-helicity index and bulk Richardson number are important in that aspect.