Yes, I would expect to see more of a difference between real daylight and a flash.
Regarding the WB differences you're seeing, that's likely due to a non-flat spectral reflectance of the Lastolite. The result is that under one illuminant (e.g., daylight) it can appear the same to the camera as the other two (the WhiBal and light gray patch of the CC 24, row 4, column 2 -- are spectrally quite similar), but can appear different under another illuminant.