<- process development engineer @ TI for 0.5um to 32nm
You seem educated about this sort of stuff. Let me ask you something...
When a transistor's volume is reduced in half, what is the average power savings and/or TDP reduction? I.E. 100nm to 75nm.
Its an effect, not a cause, so the answer is "it depends" as it is usually an engineering target to "hit" a specific level of power-consumption reduction as a matter of creating the node itself.
It is NOT the case that we build these things (the nodes) and then after the fact we are like "oh wow, good job fellas, turns out the node we just designed has a 40% reduction in power-consumption at the same clockspeed compared to the older node".
The general expectation is to deliver anywhere from 30% to 50% reduction in the power consumption when a whole bunch of other parameters are normalized (voltage, xtor width, operating temps, etc etc).
A significant portion of the 4yr development timeline is spent in the pursuit of ensuring the node delivers the targeted power-consumption reduction.
Since most products are TDP limited in their respective markets nowadays (GPU's need to be not more than 400W, desktop CPU's not more than 150W, laptop CPU's not more than 65W, etc) the power-consumption for each successive node is pretty much required to deliver 30-50% power reduction so as to enable the near doubling in xtor count that comes with the new product generations.
Think of AMD's 4870 to 5870 transition (55nm -> 40nm). Essentially doubled the xtors (956M -> 2.15B), bumped up the core clocks a bit (750 -> 850MHz), and increased load power by a little bit (160W -> 188W).
^ that's all made possible because the power-consumption on a xtor-normalized basis (and voltage normalized, clockspeed normalized, temp normalized...in other words "all else being equal") has been reduced by ~50% with 40nm over that of 55nm.
Not sure if that helps answer the question you had in mind, but it gets a little onerous to try and define it any more explicitly without the aid of some specific examples to speak too.