If you know where to shop, you can get high (90+) CRI fluorescent tubes in just about any color temperature. A lot of the manufacturers seem to have standardized on a three digit code to describe the lights, with the first digit giving the approximate CRI and the final two giving the color temperature. So a 927 tube would be 2700K with a 90+ CRI and a 641 would be 4100K with a CRI of about 60. If you buy a cheap tube without a labeled color or CRI, it will probably be a 641, which are the nasty, old fashioned ones that give fluorescent lighting such a bad reputation. 800 series tubes are a bit more expensive but give fairly good light and comparable efficiency to the 600 series. 900 series give really nice light that closely approximates a continuous spectrum, but lose some efficiency compared to the 800 series. I have 950 tubes in my remaining fluorescent tube fixtures, and they look great compared to the 641s I had before; colors really pop, and skin looks natural.
Unfortunately, most CFLs don't include a CRI on the packaging. They have to have a CRI of at least 80 to get an EnergyStar rating, but most of them are barely above that. You can find 90+ CRI in CFLs, but mostly in daylight simulation bulbs that are 5000K and above. It's too bad, because I think a lot of people would pay for higher CRI bulbs in a wider range of colors.
I personally hate the 2700K light because it's grossly blue deficient. Your eyes can adapt to a wide range of color temperatures while maintaining a visual perception that the light is neutral. Any time the light has a visually obvious color cast, it's a sign that it has a lot more of some colors than others. That applies to the notably warm light from incandescent lamps (and fluorescent lights that try to mimic them) as much as it does to 641 fluorescent lights that have a nasty green tint. You may be able to find high CRI 2700K lights, but that just means that they're doing a good job of mimicking blue deficient incandescent light, not that they're giving truly accurate color rendition.
FWIW, high color temperature is typically more efficient because it most closely matches the sensitivity of our eyes, not because it's letting through more raw blue light from the mercury spectrum. Basically, our eyes have evolved to be most sensitive to wavelengths that are strongest in natural daylight (green and yellow) and less sensitive to colors that are weaker in natural daylight (extreme blue and extreme red). Ratings of lighting efficiency take that sensitivity into account, so daylight balanced light is naturally more efficient than warmer light is.