Many light sources and LED's are defined by their chromatic yield. The fact that the emission spectrum of the White LED is different to that of filament lamp means that its yield will be less than 100%.
Old generation LEDs that emit “cold light” at around 5000K and therefore have chromatic coordinates nearer to the blue color area, are available to buy as products marked with a CRI (Color Rendering Index) of around 75%.
Those that emit “hot light” and “natural light”, are estimated to emit around 3000K and 4000K,are commercially available as products with a CRI of around 90%.