How long do AA energizer batteries last?

It actually depends on what you're using it for. For example, a camera will drain more energy than a remote control.
Approximatley 6 months to a year depending on usage. If you, say, listen to a sports radio an hour a day every day, it'll probably last 3 months. If you have a tv remote and use it every day, probably a year. The main difference between Energizer and generic is the self discharge rate. The self discharge rate is how much power a battery cell loses even if its not in use. The avergae self discharge rate is between 8 and 20 percent of totally power over a year period. Energizer is closer to 8 while generic is closer to 20.