The easiest, cheapest way to get a decent idea of the spectrum is to use a CD or DVD (we've all got at least one coaster at home that used to be a disk). The data side makes a great diffraction spectrometer. A common industrial-grade tube has great gaping holes in the spectrum; an OTT is indistinguishable from indirect skylight (the 6500K "north light" of the studio artist's dream). It's a bit disconcerting at first, probably because we're very much used to incandescent light indoors ("daylight" photographic incandescents might hit 4200K when they're brand new, and they're WAY blue compared to standard bulbs at around 2500-2800K) but it can hardly be described as "horrible".
LEDs aren't quite there yet -- at least none of the ones I've actually seen are. On the other hand, I fondly remember a time when LEDs could not be seen at all outdoors in daylight and drank power at a rate that would have left a plasma TV in an envious rage -- one had to duck into the shade and press eighteen or so buttons simultaneously in order to tell time on a thousand-dollar digital watch. The idea of using an LED (other than a laser) to illuminate anything other than itself was laughable around 1980; the spectrum problem and diffusion are trivial compared to the problems that have already been solved. It won't be long.