So since the Vcore is measured differently between these two platforms.
Incorrect, however VCore is measured differently between manufacturers, and some manufacturers show both readings.
MSI and ASRock utilize the standard VCore measurement system with no modifications, which measures voltage at the VRM location.
ASUS uses a VR VOUT style of measurement, which measures voltage closer to the CPU socket, giving a more accurate reading of what is actually being applied to the CPU after voltage losses through the copper in the motherboard. The confusion comes in the fact that ASUS has decided to label this as VCore (not technically incorrectly), without mentioning the change, which makes voltage readings appear different from Z370 to Z390.
Gigabyte has both readings on board with two separate sensors. When you set VCore voltage in BIOS, you are affecting the standard VCore measurement, however you can see VR VOUT voltage readings in Windows using a sensor monitoring program like HWINFO64.
To answer the basis of your question with these items out of the way, an ASUS Z390 motherboard will display lower voltage readings than any ASUS Z370 motherboard, or any other Z370/Z390 motherboard when looking at the VCore reading. It should match nearly exactly (or within a margin of error) with a Gigabyte VR VOUT reading.