The best replacement for cri is color temperature.

The best alternatives to cri are rated as following:
★★★★★  color temperature
★★★  cqs
★★  texmo
★★  reer
★  ckd
★  color temp
★  cct
  cdi
  neutral white

Your alternative for cri is not listed? Suggest!
Speaking about cri, one probably shouldn't forget about cfl.

Other search terms related to cri and their ratings are:
★★★★★ cfl
You have in mind a companion for cri and it is not yet here? Propose!



Google Trends

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cri
color temperature
cqs