We are sold LED bulbs as amazing achievements in energy efficiency (after a couple of other generations of 'energy-saver' bulbs to get us used to the idea). The lighting that comes from these bulbs might appear to be the same, but it is not. Incandescents are a piece of metal filament glowing from having current pushed through it. So you're looking at hot metal essentially. LEDs are diodes flashing on and off very quickly.
Our irises expand and shrink (ie. dilation) to adjust for the ambient light level, or what you're looking at. This is why your pupils are small when you're outside in the sun, and they get bigger when you're in a darker room. Flashing lights cause your irises to struggle to grow and shrink to accomodate that changing lighting environment - whether you realise consciously or not. Arguments have been made that this is why people feel more tired when spending time in LED lighting.
They have made it difficult to use incandenscents these days because houses will generally be already built/fitted with LEDs, and even desk lamp fixtures and so on are now often rated for lower wattages (e.g. max 15w) which is enough for an LED bulb, but an equivalent (less efficient) incandescent bulb would be far too weak at that wattage. You would probably want a 45 or 60w incandescent bulb, which would burn out the fixture. Very clever.
Either way, get some incandescent bulbs, find an old second hand desk lamp, and see if you can feel the difference. You're one step closer to an oil lamp or fire.. which is even more relaxing yet.