It depends on how eyes treats the light: more cold lumens will give you more details on far objects, coz our eyes significantly more sensitive to the blue part of spectre which is slightly suppressed on neutral/warm phosphors, according to cree. I have deree XP-E Q5 5C, which is reddish, not yellowish as my neutral 123^2 quark Q3 5A and around 7k lux on 1 meter vs Fenix TK12-R2 with around 8400 lux. The difference on 40-50 meters is significant. I can easily detect almost everything with fenix, and with deree there's half of details, or even less.
Regarding color rendition: surprize, but fenix shows true daylight colors, with slightly greenish cast, but once you point the light on true white object, eyes will adopt and the cast is gone.
Neutral white an cold white has the same CRI - 75.
There's not only CRI in the game, but how eyes percept light and colors - this is not the same, wikipedia will help.