.....wouldn't actually tell you much, if there were such a thing. Two objects of identical metals can have various eddy current "decay rates", based on their shape, size, and cross-sectional mass. As an example, suppose you had two 14 karat gold rings. One is very tiny in cross section, while the other is very large and thick. The larger, thicker one would have a longer eddy current decay time than the smaller one would, even if they are made of the same exact alloy composition.
In a similar scenario, suppose you have two identical rings, both the same weight and cross sectional mass. If one is "intact" while the other is broken or separated at some point, the intact ring will produce a "longer lasting" eddy current than will the broken ring.
What a PI machine does is "receive" this eddy or "remaining" electromagnetic current within the metal object after the TX signal stops and the receiver circuit is switched on.
The reason that ferrous objects react so much more strongly than non-ferrous is because of a ferrous metals ability to retain an eddy current for a longer period of time (known as a longer decay curve).... actually the induced current from the TX function of the PI "IN ADDITION" to it's natural magnetic properties.
Another example might be two gold nuggets, both of identical weight, but one being rather flat in cross section while the other is more of a "chunky" shape. The "chunky" nugget will invariably give a better signal because of it's ability to produce a longer lasting eddy current.
Back to your original question though, "conductivity" per se is the same in any two metal objects of identical compositional make-up. If you had an 18 karat gold BB shot and an 18 karat gold bowling ball of the identical alloy, both would have the same relative "conductivity", while the larger of the two would have a proportionally higher "conductance" or ability to carry a greater amount of current due to the increase in the mass of the larger object.
So you can see that "conductivity is conductivity", and relates the same with either pulse induction or induction balance type detectors. You might say, however, that the PI works off of a combination of both conductivity AND conductance, while most VLF-IB discriminating machines base their discriminating capabilities only on relative conductivity, or compositional make-up within the metals themselves. That is also why even with the best of VLF-IB machines, larger objects, no matter what their composition or alloy, can easily overload the discrimination circuits.
Remember too, that "RELATIVE conductivity" is only an arbitrary set of numbers, using annealed copper at a certain temperature as a "basis" value of 100. Every other metal is assigned a number off of that basis to indicate either a greater or lesser conductivity "in relation" to the copper.
Hope this is of some help in explaining how conductivity relates to PI.
Ralph