And if I ever pull a boner and let the batteries go dead, I have an A2 style flip up BUIS
ETA: For your two choices, I would probably go with the Aimpoint just because of the battery life. I think I have left every battery powered optic I own on at one point.
The current version F of the Eotech:
Battery Life:
1,000 continuous hours (lithium) at nominal setting 12;
600 continuous with AA alkaline