I just got my first AR and have a few questions. I have only owned handguns in the past and am trying to learn all I can about firearms. My question is what is the main difference between optics. In what situations would say an Eotech 551 or 552 be used in. And in what situations would a Trijicon ACOG be used in. What are the pros and cons about the different style of optics.

Get whatever you like best.  Chances are you're not going to be doing anything other than plinking / target shooting, and you're not going to be playing special-operations-space-shuttle-door-gunner anytime soon, so just get whatever you like.

If you need to grab the rifle in an emergency, either will likely do better than nothing, assuming you've taken the time to learn how to use it.

You are kind of comparing apples to oranges.  The EoTech is a non magnified optic whereas the ACOG is a 4X optic.  Both can be used for up close work but up close the EoTech would have the upper hand with the larger field of view  (FOV)  From a distance of 100 yards and out the ACOG becomes the better choice simply because of the magnified optics.  Both are great optics.  The EoTech runs off batteries that have very long runs times.  And the ACOG is self luminous and comes in several different reticle patterns.  Hope this helps.

Pick you gear to suit the mission.

Eotech/Aimpoint for CQB and close range in all light conditions (although you can hit man size targets beyond 100m easily) .

ACOG with 3.5x, 4x magnification for medium to long range, daytime.

I'v owned a TA11 with the donut reticle, and a compact ACOG 1.5x with amber triangle reticle.  The magnification on both slowed me down in CQB.  Also, the ACOG reticles wash out when I used a white light.  

Sorry but the ACOG reticles do not wash out, period. The reticule is chemically etched into a prism! The illumination will turn to black when looking directly into light which is best as you want a dark reticle looking into intense light. As others have mentioned these are two very different sighting systems. A better comparison to the Aimpoint/Eotech would be a Reflex sight.

Advantages to ACOG are they are battery free, virtually bulletproof (literally), provide magnification for increased target identification, provide a bullet drop compensator with built in ranging, No on/off switches as they are always ready to go, night time tritium illumination is perfect for NV use or eyes adjusted to low light conditions....... the list goes on. Field of view is unlimited in a practical sense to your sight as you use two eyes open with the ACOG just as you should be with a Aimpoint/Eotech. For a magnified sight however field of view when looking through the scope alone is very wide in the 4x32 ACOGS.

Advantages to the others mentioned....... I am still thinking I will have to get back to you. LOL. I am a little biased however.

I forgot to mention WATERPROOF. Approx 500 ft. for 8 hours last time I checked. New Orleans SWAT team during Katrina fished out all there electronic sights after the flood adn they were a no go due to all the salt water. Luckily they had quite a few Compact ACOGS which they are still using today.

These are not conditions most ACOG civilian users face, it does however show the durability of the products they own.

My examples of the reticle washing out.

During the 2006 USPSA Multigun Nationals, one stage required you to engage a number of targets, then go into a small building and engage additional targets through ports it the building.
It was very bright outside, and very dark inside.
I had no problem engaging the outside targets, but after entering the building to shoot through the ports, I had difficulty seeing the recticle.  It was still there, but it was black, as the fiber optic couldn't pick up any ambient light to light the reticle, and the tritium was not bright enough to light the reticle.

I had similar experiences when using the TA11 in CBQ training with a white light.

The Compact ACOG I owned with the amber triangle was not very visible on bright days with earth colored backgrounds and tan colored targets.

IMO, the dual illumination of the ACOGS doesn't work very well.

Paul, I highly respect what you have to say, but I was using clear lens Oakley M frames at the time.  

ACOGs are terrific optics, but they don't do what I want them to do.

On another topic, thanks Paul for your support of the G. Trauma kit, and for selling me just the DVD.  It's great stuff.  I recommended it to several friends, one of who bought the full kit.  He is very pleased with it.

Quoted: Sorry but the ACOG reticles do not wash out, period. The reticule is chemically etched into a prism! The illumination will turn to black when looking directly into light which is best as you want a dark reticle looking into intense light. As others have mentioned these are two very different sighting systems. A better comparison to the Aimpoint/Eotech would be a Reflex sight. Advantages to ACOG are they are battery free, virtually bulletproof (literally), provide magnification for increased target identification, provide a bullet drop compensator with built in ranging, No on/off switches as they are always ready to go, night time tritium illumination is perfect for NV use or eyes adjusted to low light conditions....... the list goes on. Field of view is unlimited in a practical sense to your sight as you use two eyes open with the ACOG just as you should be with a Aimpoint/Eotech. For a magnified sight however field of view when looking through the scope alone is very wide in the 4x32 ACOGS. Advantages to the others mentioned....... I am still thinking I will have to get back to you. LOL. I am a little biased however.

The ACOG is awesome, but the tritium is a bit too much for current generation NVG, it will be almost impossible to see well enought to shoot.