It's snowing and miserable, so what can you do but an experiment?
I took a fully-charged, age 0, EN-EL15 type 20; the D500 said it was 94%, the D7000 said it was 96%. I took 30 second exposures, with long exposure NR off; ISO was 100; capture was RAW, manual shutter press, AF off.
After 10 exposures the D500 said the battery was at 95%, after 20 92%, after 30 90%, after 40 87%, after 50 84% and after 60 81%. In the D7000 the battery read 86%. After 70 exposures the D500 said the battery was 77% and the D7000 said it was 84%. After 80 exposures the D500 said 74% and the D7000 82%, then after 90 71% vs 78%, after 100 67% vs 75%, after 110 64% vs 73%, after 120 61% vs 71%, after 130 55% vs 67%, after 140 52% vs 65% and after 150 exposures 48% vs 61%.
So, as exposures accumulate, the apparent battery drain per 10 exposures in the D500 is probably the same, although it might be increasing slightly, from 2-3% of the charge at first to 3-4% after 150 exposures. Why that might be I do not know. The D7000 clearly recorded more charge at all the levels tested, and the gap between the D500 and the D7000 increased as the number of exposures increased, from 5% after 60 exposures to 13% after 150.
I put another fully charged battery in the D7000, where it read 95%; the same battery read 92% in the D500. Settings were the same as for the D500 trial. After 10 exposures in the D7000 the battery read 93%, after 20 92%, after 30 90%, after 40 88%, after 50 87%, and after 60 86%. At that time the battery read 80% in the D500 and I stopped.
So there seems to be no big difference in power use per exposure in the D7000 and D500: after 60 exposures the battery read the same whichever camera it was used in. The D500 consistently reported less % charge than the D7000 at the same level of charge, and did so to a greater degree as the charge declined, so that seems to be the main cause of the reduced effective life.