I once read that they are more efficient than LEDs.
This is not the case anymore, LED's efficacy already exceeded the small fluorescents.
The CCFL use was confined to lower power illumination, requiring longer, thin tubes (TV/monitor backlights), frequent switching (advertisements) and/or where custom shapes are required (advertisements).
The useful life of the tubes is way longer with frequent switching than the ones with hot cathodes, but the reliability of the ballasts in small format (retrofits for incandescents) become way worse than the hot cathode lamps (it require really high voltage in multi-kV range), so the ballast tend to limit the useful life.
Moreover the CCFL ballast is way more complex (mainly due to the need of the high voltage), what make it way more expensive.
On the other hand the cold cathodes make the CCFL ideal for custom shape tubing, where the lamps are made manually, because they are quite robust in handling (no sensitive coat), need only the basic gas cleanup, but do not need the tricky and quite sensitive step of cathode activation necessary for hot electrodes, what could be practically made only using an automated machinery.
But even there the LED's are slowly taking over, as their dot format allow greater design flexibility and lack of HV and fragile glass tubing make the assemblies way easier to build and handle.