Can't go wrong with either one.
Aimpoints have the best battery live for constant on. If you change the batteries out every 2-3 years on your birthday you should never worry
EOtechs (some if not all) have auto shutoff. So they still last a while with that feature but it's one more thing to remember on a HD or Duty rifle.
I went with Aimpoints because of battery life and weight. But I just picked up a used EOTech.