My tint preference changes depending on what my eyes are adapted to.
During daytime, Cool White looks like a match to my eyes white balance, and seems white
During the evening with house lights on, I prefer Neutral White, it seems white, and Cool White seems blue
At night, when my eyes are fully dark adapted, I prefer Warm White, it seems white, and Neutral White seems blue
Cool white will have more lumens than Neutral, which will have more lumens than Warm.
Here is an example,
CW at 6000k
NW at 4500k
WW at 3000k
the NW is 75% warmer than CW, and will have 75% of the lumens of CW
the WW is 50% warmer than CW, and will have 50% of the lumens of CW
in a fully dark adapted setting, I also prefer lower lumen levels
in sunlight adapted setting, I prefer the highest lumen levels
here is a concept group, imagine a light with 3 leds, that each only turn on to one of the 3 LMH modes:
WW at <5 lumens for full dark adapted vision (it will not look orange when fully dark adapted)
NW at <40 and >5 lumens for incandescent adapted vision (it will look white when eyes are adapted to incandescent light)
CW at 100+ lumens for sunlight adapted vision (it will not look blue when eyes are adapted to sunlight)
Cool white is good for throw, and for working on cars during the day, but CW is almost always Low CRI, so it is poor at rendering Red, such as in the following pic.. Note the hand looks pale and dead
here is what High CRI does (High CRI, above 80, usually means the LED will also be Neutral or Warm. For example here is a High CRI shot of my hand, note the more natural red tones:
By contrast working on a car outdoors, the CW is MUCH brighter and therefore shows more detail. Note that the tint does not seem blue, it closely matches the sunlight seen beyond the car
otoh, giving up 50% of the lumens to increase Red rendering Fails to be practical during the day, and note that the tint appears orange (because eyes, and camera, are white ballanced to the sunlight beyond the car:
So, when someone says they dont like Warm tint, chances are they are trying to use it when their eyes are whitebalanced to sunlight. When someone says they dont like Cool White tint, chances are they are trying to use it at night, when eyes are whitebalanced to Neutral or Warm ambient light.
I have an LED lamp in my kitchen (Phillips Hue), and it can be made to produce 6000k light or 3000k light. Here is an attempt to show how that affects our perception of a 3000k LED on left and a 6000k LED, against a 3000k ambient backgrond: (note how blueish the right hand beam is)
Same lights, but with a 6000k background, note the CW light does not look blue, and instead the WW looks orange.
moral of the story, I prefer Warm in full dark, I prefer Neutral indoors after sunset, I prefer CW outdoors during the day.. which is why I have more than one light...
fwiw, all these examples are single AAA lights.. here are my 3 LEDs shining on a piece of printer paper folded to a 90 degree angle (camera is choosing its own white balance based on the relative tints, it is a good match to what my eyes see when I turn on all 3 at the same time)