CRI is how well color gets reflected, LEDs come usually from 70s to 80s, but high CRI options are not uncommon (CRI over 90). The higher, the more vivid, but it’s a matter of personal preference how much weight you give to CRI when selecting an emitter.
Tint shift is the difference in tint from the center of the beam to the outer edge of the spill, and this changes with LED, reflector/optics type and material, weather the emitter was dedomed or not, if the front glass has anti-reflective coating or not. If the hotspot is blueish, the corona gets yellow and the spill gets green, for example, it will be an ugly light, so ideally you get the tint you prefer with little shift as possible
In my experience, CRI matters very little. I suppose its helpful if you’re viewing art or are a photography, but in most cases its irrelevant.
On the other hand, Tint makes a much bigger difference. Cool tints make outdoor terrain look flat and are harsh on the eyes. Neutral tints look much more pleasant and make it easier to resolve objects you’re looking at. Warm tints are also very pleasant outdoors, but look too orange indoors.