For all intents and purposes, there's no difference between the EoTech and the Aimpoint.
The Aimpoint is SLIGHTLY more durable, and has a better battery life (especially so with the newer models) - the EoTech has a better field of view and takes (with the right model) cheaper / easier to come by batteries.
I've got both, I use the Aimpoint.
If your eye picks up the circle on the EoTech, that's a GREAT way to go. My eye instinctively looks for the dot, and the 1 MOA dot of the EoTech isn't fast for me. The 2 MOA dot on the Aimpoint is fast, and I can hit reliably to 500 yards with it. Not good hits, but hits none the less - but at 400 the hits are GOOD.
With the 4 MOA Aimpoint, I had difficulties hitting past 300, and every now and again I'd drop a shot at 300. It's the dot, which covers so much of the target at that range it was hard to get on and stay on.
FWIW, neither the EoTech nor the Aimpoint has a good mounting solution out of the box. The EoTech either wants to come loose unless loctited (which I don't do) or requires a QD lever mount. The ARMS QD lever mounts are rubbish, they shoot loose over time. Likewise, the A+ answer for the Aimpoint is a LaRue mount.
What size dot you get depends on what you're going to do with it. If you're only hitting inside 300, then the 4 MOA will be fast-fast. Interestingly, my M2 with the 4 MOA dot wasn't any faster for me than the M3 with the 2 MOA dot - maybe it's just me. Anything larger than 4 MOA will decrease your effective range further.
The EoTech is a nifty tool. If I could center my eye on the circle instead of the dot, I'd call it the best all-around. The 1 MOA dot allows precise hits past 400, the circle (if I could center on it subconsciously) would be fast-fast for up close.
Hope that helps!