Quoted:
I have a good understanding of how reflex (or red dot) sights work. Basically, a light source, usually a laser or an LED (in the case of Aimpoints to conserve battery life) shines a light at the front lens. The front lens is engineered to reflect the light back towards the user, which is what the user sees as the reticle. You may have noticed that the front lens on these sights have a greenish tint when you look through the sight, and the lens has an amber/yellow/red tint when you look at it from the front. This is to help the light reflect back so that it does not simply pass trough the lens.
The reflected light must be collimated, which means all reflected rays are nearly parallel to another. This way, no matter how you look at the light, the reflected ray is parallel to the axis of the bore (assuming the sight is properly zeroed). Collimated light is a feature that let's manufacturers advertise their sights as being "parallax-free".
The reality is that no sight is 100% parallax-free - it is impossible to achieve and defies the laws of physics. However, good optical engineering can reduce parallax to the point where it won't affect the placements of your shots by more than a few inches. The light must be collimated as much as possible so that the sight is virtually parallax-free.
The magic lies in the front lens. It is highly engineered to reflect as much light as possible without relying too much on tinting. Poorer quality optics rely on heavy tinting in order to ensure that the light will reflect, which makes the front lens dark and harder to see through. An Aimpoint, on the other hand, has less tinting than most other offerings because of the well-engineered front lens. Also, the lens must be designed to collimate the light as much as possible in order to reduce parallax, something that Aimpoints achieve well. You may have heard Aimpoint advertise the advantage of their "dual-lens" system. It means that the front lens is actually two lenses pieced together. This is an optical feature to reflect the light better (i.e. not rely too much on tinting and ensure the light is as collimated as possible). This does not refer to the fact that there is a front lens and a rear lens to keep the optic contained within a tube (this is just to protect the optic from physical damage and to shut out sunlight so that it does not wash out the reticle).
I found this image of how EOTechs work.
http://upload.wikimedia.org/wikipedia/commons/c/c0/Litepath.jpg
I'm not as knowledgeable with EOTechs, but I can see a lot from this picture. It relies on the same principles as reflex sights (reflection, collimation, etc). Remember that reflex sights rely on a lens to reflect and collimate the light, while the EOTech can use a mirror. This eliminates the need for tinting, and when you compare an Aimpoint and an EOTech side-to-side, you will notice that the EOTech's window is much clearer and easy to see through.
My local gun shop owner attributes a lot of the disadvantages of an Aimpoint to problems associated with using a lens as a reflector/collimator. The lens must be smaller, or there will be parallax, thus reducing the size of the viewing window. The lens must be tinted or light will pass through the lens without being reflected back towards the shooter. Also, when the lens is exposed to sunlight, it will wash out the light that is being used to produce the reticle. He says EOTechs solve these problems - no tinting, larger window, and no reticle wash-out.
The EOTech does require a laser to produce the hologram, which reduces battery life. An LED is not strong enough.
Hope this helps :)