Well, the unwelcome advice would be "both".
The RCBS Precision Mic actually measures case head to shoulder datum, using SAAMI dimensions for zero. The "prototype bullet" and separate dial is supposed to permit measuring distance to lands, but as the prototype bullet isn't the one you are actually using, this may or may not work. (Many, I have read, use the RCBS Precision Mic for the first purpose and toss the prototype bullet stuff.)
The LE Wilson gauge is often used as a "drop-in" gauge to check for case head to shoulder datum (often called cartridge headspace), by looking at the head relative to a step cut in the bottom of the gauge. It also works to measure "trim length" by inverting the gauge / case on a flat surface and observing the case mouth at the other end, where there is a second cut step. The instructions describe how to use calipers in conjunction with the gauge to measure fired cases and resized cases.
I believe both gauges are deliberately oversized in diameter at the body so that there is no interference with measuring fired cases.
If I had to get just one, I'd get the LE Wilson and use it with calipers. When used as a drop-in gauge, it is fast enough to check an entire batch of brass for cartridge headspace and trim length. For setting up the resizing die initially, it can be used with a caliper instead of just "eyeballing" the head relative to the steps.
But the RCBS Precision Mic is a nice tool, too. Just not as versatile, IMO.
(Can't help with the rhetorical question...
)