Gas tube signs have a very unique spectral emissions that makes them appear the way they do. Very little effort has been put into LED lighting to properly mimic the appealing spectral emission of incandescent filtered or gas tube colored lighting.
Almost exclusively phosphor coatings have been tuned to cause blue and near UV leds to emit (sort of) broad spectrum white light and nothing more, though it would certainly be possible to develop a phosphor that could more closely approxmiate neon, for instance.
As for direct emission, red green and blue LEDs are mostly now only available at certain wavelengths for tricolor mixing applications. Due to economies of scale, LEDs at other visible wavelengths are extremely underdeveloped technology.