There are a fair number of threads doing this. I'm on lunch, so I'll grab a few. My understanding is:
0. Most lights are analyzed and compared to blackbody sources. This lets scientists model them fairly easily, but it does not describe light well. CCT tells you what blackbody it is like, and CRI tells you how like that BB it is.
1. All discussion of color perception is valueless without using objective results OR standardized subjective studies. I can show you a 630 nm LED that is 'Red as red,' until I show you a 660 nm red. Then the old red is so orange you'd call it a yellow-orange US caution light, not red.
2. Sunlight is markedly different from radiation from a black-body source. It has spectral lines coming from the star and is filtered and scattered. Further, 'Sunlight' at the ground varies based on weather, time of day, elevation, latitude, and time of year.
3. Color perception is complex. "Color Rendering Index" certainly does not capture the full gamut of color perception, nor of white light perception. Different CCTs of black-body-like radiation are appropriate for different tasks, and the human body takes important circadian cues from changing CCT throughout the day and night.
CRI of White LEDs
Making a desk lamp
"When 2700K is not 2700K"
What Color Spectral Power Distribution produces the best photography?
Ultimate Light Bulb Test: Incan, Fluoro, LED
Now for my experiences:
1. Incandescent light changes dramatically depending on whether the bulb is driven over, at, or under its rated voltage. Most people classify these as:
Under: Yellow or orange (CCT is 2300K to maybe 3000K? Wild guess)
At: Yellow or white (Great, huh? This is the trouble with such subjective views, CCT is 2800K to maybe 3500K)
Over: Pure white (3500K to 4000K? I forget when tungsten melts)
I know of some LEDs that could match each of these conditions. However, LEDs have CCT, CRI, and tint bins as well, and their tint and CCT change greatly with varying drive current and temperature. Cree tint bins tend to be big enough to park six trucks on, but I find that:
1. "High CRI" warm white Crees look rather like underdriven or correctly-driven filaments. Depends on who you are and what filaments you look at.
2. "Neutral white" Crees (Especially, to my eyes, in the 5A to 3C range) look like correctly- to over-driven filaments.
3. "High CCT" high CRI LEDs, like Nichia's well-known offering, look much like near-noonday sunlight to my eyes. But it would depend on the day.
Sadly, I can't find the two I had in mind. Harrumph.