I hope this isn't way too much for a reply...
Everything I am going to tell you is pure opinion. I have never served in the military, nor am I a LEO. However, I have had some training with the AR's and about 2.5 years of experience with them. I am far from an expert and possible the guy who use these for a living can either confirm or correct me if I miss something.
There are several kinds of red dot sights (RDS)... or what people consider RDS. Unfortunately names like RDS and holographic are interoperable and accurate to a degree.
You have battle quality holographic sights like the EOTech EXPS, Reflex sights like Leupold DeltaPoint (still uses a hologram) and then true RDS like the Leupold and Aimpoints (still uses a hologram) mentioned above. They all have there advantages and disadvantages.
The trick to rapid target acquisition at close range has little to do with your sighting hardware. There are two main things to focus on. One is lighting/visibility... can you see your target? The other is going to be practice... period. Amateurs practice until they get it right. Professionals practice until they can't get it wrong. In fact, I have friends that are so proficient with AR's at close range, that while clearing a house or building with a flat-top M4A3 with no sighting hardware, that they will still be on target every time. They have practiced so much that the muscle memory wont let them make a mistake.
Obviously, for home defense, the typical Joe won't train that much. You still need lots of practice though. And use a range or sign-up for events that get you moving on your feet, shooting while in motion and responding to animated targets... not just static in a booth.
Okay, now that the "training lecture" is over... lets talk sights.
Fixed and Flip-up Sights -
As mention, get used to using these. Batteries die, electronics fail. I typically recommend round frame sights like the Troy Micro M4 front & doa rear folding sights. Because everything is round, it i very easy to shoot with both eyes open and acquire a good picture. You will need to work with someone who knows how manual battle sights should be set-up so it is done and you are trained correctly.
Pro's - No batteries, easy to use, hard to break.
Con's - Hard to use black sights in low light, can be slower target acquisition compared to digital sights.
Red Dot Sights -
Pro's - Slightly larger aperture than manual sights, faster target acquisition, good for low light and daytime, brands like Aimpoint have 4 or 5 years or battery run-time, durable.
Con's - with the smallest aperture opening and largest body of all digitals, they will obstruct your forward view the most and have the most sensitivity to head-to-sight alignment.
Reflex Sights -
Pros - Smallest and lightest option, larger opening with the slimmest aperture hoop causing the least amount of view obstruction for faster target acquisition, more forgiving to head position, good in day/night conditions
Cons - Shorter battery life, can be damaged more easily, quality reflex sights tend to be more expensive than a quality RDS.
Battle Quality Holographic Sights -
Pro's - Intermediate battery life, extremely durable, largest aperture and very slim hoop for extremely rapid target acquisition, very forgiving to head position, good for day/night.
Con's - Compared to the previous types, they are heavier, more bulky, expensive and really limited to EOTech for quality products.
On my M4 I started off with an Aimpoint, switched to a Reflex, and then to a EOTech. Now, I don't use any of them. I am using flip-up sights and an under barrel laser/flashlight combo. The red laser is not good past 20 yards outside during the day... but I feel this is the best home defense configuration I have had so far.
I did keep the Reflex on my MP5 though.
In this picture, the light/laser is on the side. I relocated it under the barrel to get rid of shadows to my side.
My Aimpoints...
EOTech
Classic Reflex
