Kaman_anand Everything which lights up drains the battery, even the Glyph lights have a tiny impact on battery life.
The AoD neither hurts the longevity of the screen (hence the moving content) nor the battery. It's just another small consumer when it comes to power.
By the way when the phone is being faced screen down, the AoD gets automatically disabled anyways. It also gets disabled if the proximity sensor is covered, so if you habe it inside a pouch or pocket, chances are fairly high it's disabled.