What makes a laser more dangerous than a high powered single color LED for example?
Is it the fact that it's coherent light, all the photons have the same wavelength, that it can be focused to a small spot, or some combination of the above?
Would I need laser safety glasses when working with high powered LEDs?
The Sun can damage your eye by delivering a few tens of milliwatts of power to your retina. A laser of modest power can deliver more than this.
The Sun is resolved: its power is spread across thousands of photosensitive cells. The lens of your eye can concentrate the power of a laser on a few cells, so even a low power laser can injure you.
You perceive the Sun as bright, and you instinctively avoid damaging your eyes with it. You can't see the light from an infrared laser, so those are particularly dangerous.
For working with a high powered LED, you may need specialized safety glasses, but you need to consult the relevant safety standards to decide exactly what you need for your specific situation. Details matter. It's not a good question for this forum.
The answer actually is kind of obscure. It's because laser light has extremely low etendue. In practical terms, it means that all of the light from a laser seems to come (or can be made to seem to come, using geometric optics) from an infinitessimal point, that is very far away.
That property allows laser light to be shaped (again, by geometric optics) into an intense narrow beam, and it also allows it to be focused onto an extremely small, extremely intense spot.
If you are unlucky, and a laser beam enters the pupil of your eye, nearly all of the power of the laser can enter your eye and be focused onto a very small spot on your retina.
There are other dangerous light sources (hint: Don't stare at the Sun or peer into a blast furnace), but in order to be so dangerous, they must have much more total power than the laser. It is not possible for such a large fraction of the light from any other source to be concentrated onto such a small spot in your eyeball.
A main reason that laser light is dangerous is that it can easily be focused down to a tiny spot.
If you try to use a series of lenses to focus light from a standard lightbulb, you will find that you are limited in how concentrated you can make it. There is a property of a light source called etendue, which is related to the size of the source and the angular spread over which it emits light, and this is conserved by optical elements such as lenses. For relatively large sources that emit in all directions, this limits how well you can "collect" the light.
Lasers often have very low etendue. The fact that their light is emitted into a single mode makes it easy for it to originate from a tiny point or a uniform beam. Furthermore, the fact that it is monochromatic - that is has a single wavelength - helps to focus it because lenses generally have chromatic aberrations. As such, you can focus a laser to a very intense spot, such that a laser of one watt, much less power than a lightbulb, can generate light intense enough to start fires. Your eyes also themselves focus incoming light onto your retina, so they can potentially focus laser light into a more intense point than other sources. That said, this gives lasers the potential to be dangerous, rather than guaranteeing that they are. If you don't focus the laser light down, it is not necessarily more dangerous than any other source.
Incidentally, sunlight also has low etendue- by the time it reaches us it is barely diverging at all. That is why you can also focus down sunlight with a magnifying glass and start fires. So lasers are not unique in this regard, but they are more dangerous than most other sources of light.
There are other dangers associated with lasers as well. For example, some lasers are in an invisible range, but such lasers can damage your eyes even though you can't tell they are shining on them.
The dangers I've described are generally reduced with visible range LEDs, but any type of light can be dangerous under the right conditions. You should look for specific guidance for the particulars of your situation.
