Just testing ... the Lumetri/FC difference seems to be between 0 and maybe 4* or so of hue. When there is a difference, the Lumetri is towards yellow a titch, FC towards red. A very small amount but measurable.
FC ... hath some issues in the math in a couple places. I avoid that religiously.
Also, I used to use a white-card more than now, as all that does is match white-points. If you have a cast all through the image, it doesn't do anything about matching mids/shadows. This is of course common across all apps, Resolve is the same. So a white-point is only really a starting point for removing color casts.
For my first pass neutralizing clips, I tend to actually use the Shadow/Highlight "tint" wheels of the Creative tab more while watching Vectorscope YUV. Rarely bother with white-point.
Also, in the Basic tab's Temperature & Tint controls, the Temp control balances R/B channel white points against each other, the Tint channel balances R/B white point against G white point. Just for general information. Again, watch the Vectorscope YUV when working with that as much or more than your image.
Neil