The biggest difference is the way that each of these sights creates the point of aim that you use to put your rifle on target.
Red dots use a small LED that is reflected by a parabolic lens at the objective end of the optic. This means that when you are looking through the optic, you are looking through the lens that is reflecting the dot. Due to the curvature of this lens, and the necessary design of the housing and placement of the LED emitter, the size/shape of a red dot is somewhat limited by physics. Generally speaking, to avoid a lot of blue tint around the edges or fish eye effect, the larger you try to make the field of view through the actual optic itself, by making a larger opening, the longer and more bulky the sight needs to be.
Pros:
- Longer battery life (LED's draw less from your battery)
- Very simple and user friendly
- There are many options from tiny open-top red dots to full-sized enclosed red dots for just about any application
Cons:
- Some image distortion from the objective parabolic lens
- Limitations of reticle design
- Limitations on size - can't simply make FOV bigger without making the sight bigger too
Holographics, on the other hand - The thing responsible for creating your point of aim in a holographic is not something that you actually look through like the lens in the red dot - it could be located in the bottom/base of the sight or on the roof of the sight, but either way, will be out of your field of view. The laser emitter reflects a number of times throughout the system, picks up the hologram (Reticle), and pops that reticle right in your field of view. This offers a few advantages - you can essentially make any pattern you want on a hologram (Hence the reason holographic sights tend to have more involved/versatile reticles). Perhaps most notably - it means that you don't have any image distortion whatsoever with a holographic sight, regardless of size or shape, because you aren't looking through any type of optical element or lens at all - just windows, essentially. [Unique to only the UH-1 holographic sight, the system is even designed such that you could completely remove both glass windows on either end of the optic and the reticle would still be floating right in the middle of the housing and would be perfectly usable.] This is part of the thing that gives holographic sights such a "Heads up display" type feel - they can have larger openings for a bigger field of view, and have a perfectly flat image that looks just as it would with your naked eye - there's just a reticle floating right in your line of vision.
Pros:
- More reticle options
- Zero image distortion
- More heads up display type feel
Cons:
- Shorter battery life (Laser draws much more from the battery)
- Less options - nothing for pistols for example
- It's not that they are user-unfriendly, but often times with the reticles, there are more things to learn about the sight before using it to its max potential
Hope that helps explain it a bit
Jimmy H