Can't go wrong either way
They're both top-of-the-line sights. The human eye is considered to have a resolution of about 1 MOA. Mine aren't that good, but it any case the 1 MOA dot is more like looking at a star-- its apparent size is relative to its brightness. Aimpoint now makes most of their sights with an optional 2 MOA dot, which is still pretty much "infinitesimal".
For some people it will come down to the controls. The EOTech is pushbutton controlled. You press any button to turn it on, then there are "up" and "down" brightness buttons. The 512 and most other models have the buttons on the back, but they have new ones with side-mounted buttons, which I prefer. Aimpoint has the rotary on-off-brightness control, which some prefer.
The Aimpoints can be mounted lower, which matters not at all on an AR flat top, but it is worth considering in most other applications (you didn't specify receiver type). The EOTech will be the correct height on AR flat tops as it comes from the box. Aimpoints need a tall ring (QRP with spacer, ARMS#22 with full spacer, etc.) unless you go with the newest CompM4, which comes with its own mount and its own spacer, which works nicely on the AR flat top.
The EOTech reticle is about the best there is, but I would also consider the Chevron in the Trijicon TX30 or RX09 as being ultra-cool reticles.
Having used all of the above (my company sells them) I could not be persuaded to become unhappy with any of them.
The new magnifiers are pretty interesting too. Be advised that the Aimpoint magnifier mount height (Twist lock with the spacer from the QRP) works best with the EOTech 512, et all as well as the Aimpoints. There is a height difference, so the EOTech magnifier works best with the EOTech 553, which is 7 mm higher than the other EOTechs. Any of these reflex or holosights give a stunningly crisp reticle with the magnifiers.