I had a third-party AOD on my Galaxy A01 during the short time I used it, but I still prefer the Galaxy S4's 'Air View' glance. You wave your hand over the phone and it lights up similar to the AOD, showing battery, notifications, missed calls, messages, and the time. I prefer that since it lessens burn in, looks nicer, and is cool to show off. Doesn't require touching or the battery drain. Sadly, only my Note II and S4 support it. My S4 Mini, S Relay, and SIII do not.
Still prefer the LED notification over an AOD, since I know at a glance what the blinking light means by color (apps help with this, expanding the capability). I don't have to be close to my phone either, like with an AOD. I can see what I'm missing or not, or the charge status of my device across the room.
The A01 didn't have an OLED display, but the third-party app wasn't hitting battery nearly as hard as I'd had thought, but it was infinitely customizable, can be turned off at a certain % battery or time of day, or show for x minutes after last notification received, and had a 'fake' LED notification light as well.