This will be an interesting thread. I forsee much sackriding.
I've used both Aimpoints and EOTechs, and I bought an EOTech. The Aimpoint is nice, and there's nothing wrong with it, but I like the EOTech more. The tubular design of the Aimpoint makes looking through it more like looking through a scope while the EOTech's design really makes it look like you're looking through a floating piece of glass. It's not terribly noticeable in bright light, but in lower levels of light you get a better view through the EOTech. I also like the idea of the 65MOA circle and 1MOA dot for both fast target acquisition and more precise shooting, with the Aimpoint you're stuck with a "one size fits all" dot. The Aimpoint has better battery life, but I don't ever think a 1000 hour battery life with the EOTech is going to be a real problem. I'm sure I can come up with more if I really think, but this is just off the top of my head. They're both really good sights, I just prefer the EOTech.