What are the advantages of CMOS operational amplifiers vs bipolar in the same class?
CMOS generally have lower offset currents, but larger offset voltages. Power consumption increases with GBW, no matter the technology.
CMOS has intrinsically worse noise compared to BJTs, but this varies to much across the different op-amps that one cannot judge the noise performance based on IC-technology alone. But CMOS tends to have higher voltage noise, and lower current noise.

Rail to rail output is a cool feature, but it comes with some trade-offs in linearity. (See The Art of Electronics, chapter 5.9) And these configurations also have significantly higher open-loop output impedance.

Further reading in Art of Electronics Chapters 4 and 5.