Hi Michelle
The short answer is that, with regard to eye health, there is no evidence of a difference between LED and fluorescent light bulbs.
Here's the long answer:
Let's first take a look at LED and fluorescent bulbs. With regard to household use, we desire white light (including cool white, daylight etc). Each individual LED diode/chip can only emit a narrow band of wavelengths of light ie it generally only emits light of one colour. In order to get white light, either multiple LEDs are used of different colours (red, green, blue) or a blue LED is used in conjunction with a yellow phosphor. This leads to a 'spike' in the blue end of the emission spectra of these lights, of which the proportion is variable. Note that the overall effect obtained is a white coloured light, just that if you split the light up (eg using a prism), the blue part of it tends to be a bit brighter.
Fluorescent lights work by emitting ultraviolet light (by running electrical current through mercury vapour), which shines on phosphor coating the tube. The phosphor then emits light of various wavelengths and spectra depending on its exact composition. Commonly used phosphors tend to emit less blue light as a total proportion of the light emitted.
And this is where I believe the concern and controversy originated: The amount of blue light emitted.
Blue light has recently become much maligned, and blamed for many things including retinal damage, macular degeneration, 'digital eye strain', and sleep pattern disruption.
If we take a step back, actually blue light is everywhere, including sunlight. The amount of blue light we get from LED lights is probably not as much as what we would get by stepping out into the sunshine everyday. In other words, even with LED lights the amount of blue light we get is very unlikely to reach a level that is damaging to the eyes. Research studies that show cell damage from blue light generally do so in artifical laboratory conditions that are totally different to real life.
There is more evidence, however, regarding how blue light might affect sleep cycles/circadian rhythms. Some research has shown that blue light suppresses melatonin more than other wavelengths of light, for example. In this regard, it might be a good idea to have warmer coloured lights/fluorescents in bedrooms, and not to stare at computer screens too late into the night, to reduce problems falling asleep at night.
