Is there a Right White for Museum and Gallery Lighting?

For the last two decades, the choice of light source for gallery lighting seemed straightforward. Specifying spotlights for a conservation gallery almost always meant using low voltage tungsten halogen. Now the go-to technology in gallery lighting is LED and suddenly the goal posts seem to have shifted. Colour rendering and colour temperature are positive choices. How do we make these decisions and are the colour metrics we use actually describing what we really see?