I'm assuming you have two light sources and want to compare their colour appearance. If you know the spectral power distribution of the light sources you want to compare, you can simply calculate the chromaticity coordinates, and then the Euclidean distance in CIE 1976 (u', v') chromaticity diagram. For the calculation steps and difference specifications you can refer to:

CIE 15:2004 Colorimetry

Colorimetry: Understanding the CIE System by Schanda

CIE TN 001:2014 Chromaticity Difference Specification for Light sources 

For the efficiency of a light source, you should be looking at the luminous efficacy (i.e. the ratio of luminous flux (lumen) emitted by the source to the input electrical power (watt), and the luminous efficiency of radiation (LER) (i.e. ratio of luminous flux to radiant flux). For the formulae, you can take a look at

Color Science: Concepts and Methods, Quantitative Data and Formulae by Wyszecki and Stiles

Dear Dr. Alp Durmus

Thank you very much for your answering. Hope, it would help me for understanding CIE.  

Thanks in advance. 

Best regards,

M Z Kadir Roni

Related to this, chromaticity alone will not tell you about the efficiency of a light source (i.e., luminous efficacy), but there are relationships between chromaticity and the maximum theoretical luminous efficacy of radiation values. MacAdam calculated these values in 1950 and there is a chart online at: https://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/chap16/F16-08%20Max%20efficacies%20&%20chromaticity.jpg