I have a number of AR15s with Aimpoint ML2s and M3s on them. I have both 4 MOA dots and 2 MOA dots. I have shot them from three feet out to 500 meters on paper.
First of all, let me say that in my opinion and in my experience, the 2 minute dot defeats the whole point of having a dot optic on the gun. As was mentioned, the point of the dot optic IS NOT to shoot tight precision groups on paper targets. In my seldom humble opinion, I think the 2 minute dot is for people who really want a scope but don't think it is tactical enough for them (they want to look like the GiIs in Iraq but really want to be shooting a scope). This whole problem comes from people being locked into the idea that tight groups are good. In some shooting sports they are. For self defense they arn't. The dot is to make rapid hits to the center of mass on a human. Making rapid hits means having a big dot that you can pick up instantly. If you happen to find yourself in one of the better known shooting schools, one of the first lessons you will be taught is that the opject of the game is to shoot handspan sized groups, COM, as fast as possible. When you start shooting tight groups on the paper, they know you aren't shooting fast enough. Defensive shooting (along with IPSC, IDPA, 3-Gun etc.) are a constant struggle between speed and accuracy. You always want more of both, but the two things usually work against each other. In defenisve type shooting, a 5-6" group is good enough. Having all your shots go through one hole actually may not be as effective as four shots each a couple inches apart.
That being said, this doesn't mean that you can't make some pretty precise shots with a dot.
I have no idea how many times I have posted this, but if you are worried about the dot covering the target, you have your optic zeroed incorrectly.
Let me offer you an example. Let's say you are shooting iron sights. The front post quickly becomes wider than the target. When this happens, you don't just give up and say the sights are no capable of hitting the target: instead, you simply put the target as close to the center of the front post as you can. Likewise, you don't zero your iron sights so the bullet impacts in the center of the front post (vertically). You zero your iron sights so the target is sitting on top of the front post either 6 0'clock or point of aim/point of impact.
The dot is no different. For precise, longish range, think of the dot like you would an iron front sight. You put the exact spot you want to hit at the very tip top of the dot. Remember your high school geometry days ? They told you that a concentric circle met a line or another circle at precisely one spot. That infinitely small one spot is the very tip top of the circle. That is the point you zero your sight to hit. At close range, for quick snap shots, this is close enough. But on long shots, if gives you a precise point to place on the target. Let's say you are shooting a silhouette target at 200 yards. You would have the dot positioned, so that the top of the circle cut the center of the "A" zone instead of covering the "A" zone with the dot.
I also highly recommend the LaRue mount and the Troy BUIS. This is the stuff you buy when you decide to forget the notion of trying to save a few bucks by buying inferior gear. In other words, both items are top of the line.