I'll do a simple pro and con list. They both share top notch quality, ultra high durability, and hold zero no matter the hell you'd put them through. So you can't really go wrong.
> Aimpoint
PROS
Different models = different purposes. Suit your needs to size/weight/other necessities
A single dot versus a crosshair/donut and dot the Eotech uses
Economy version available at $350, good price and Aimpoint quality
MOST IMPORTANTLY - Battery life. 3-5 years constant on depending on model. I leave my aimpoint on 24/7 in the safe so it's one less thing I need to do during a home invasion. I like not having to worry about this too, I imagine having the optics going out in a combat situation could potentially be life-threatening
Mounting options based on your needs. I have a great co-witness sidemount for my Aimpoint on my AK. If you want it raised, very low, swivel, quick detach, side mounted, you have any mounting option you want as there are tons of third party mounts
CONS
More expensive
It's a tube style compared to the hologram. The longer the tube the worse your sight picture will be, which the aimpoint PRO lacks compared to the micro ones
>Eotech
PROS
Holographic style sight, same overall length but the length of the glass is shorter. Gives a MUCH better picture of the target as a result (I find myself way more accurate with it)
Donut and dot style reticle. It's quicker to lign up a target and I've noticed it's way easier to see in bright conditions compared to the aimpoint
Slightly cheaper
CONS
Very short battery life
Different models have minimal differences but giant price gaps. NV compatable, buttons on the side or the back, AA or the C123 whatever batteries. Huge price gap.
Look ugly as ****, in my opinion, and also seem GIGANTIC on most rifles
Fewer third party options
VERY SHORT BATTERY LIFE
In my opinion, I'd go with the Eotech every time. The sight picture and the difference in my accuracy with it was just 10/10. I could see everything, meanwhile with my aimpoint I have a worse sight picture. It's still good, with infinite paralax, and I hit really well at 100yd with my AK.
However the Eotech has a dealbreaker, 16hrs of battery life versus 50,000 hours of battery life. I can't leave the Eotech on and I'd be afraid of having to swap batteries every other day. When they get their shit together with battery life, I have no doubt Aimpoint would go broke that day. But until then, I buy these optics on a need basis. My AK is my everyday rifle, I'd use it in SHTF, home defense, and practice with it regularly and I use an Aimpoint. I'd prefer an Eotech on my AR, which I don't use much, so having the thing going 24/7 isn't an issue for me really.