As someone very familiar with the Android world, here's why you (probably) don't want to see Apple move over to an OLED panel:
As most of you know, Samsung is the leader in OLED panels right now, with their Super AMOLED panels in the S6/Note 5 lines. All other OEMs that use OLED source them from Samsung (aside from LG, which uses their own P-OLED panels when they don't opt for LCD, which is only on their G-Flex line of smartphones).
The problem is, Samsung does not source other OEMs with the same S-AMOLED panels, but rather with B-stock panels manufactured from the year or two prior. So no other OEM that has an OLED display matches what Samsung uses for themselves. This leads to a market where Samsung's panels in their own devices are the best available mobile displays that are possible at any given point, but other OEMs OLED offerings do not match, hence why most other Android OEMs are opting for LCD panels, since current LCD panels would outperform an older OLED panel.
So, I would suspect that, IF Apple was going over to an OLED display, nobody should expect it to be as good as what is in the S6/Note 5.
I'm an Android fan, but I am moving over to the 6S Plus this cycle for other reasons. And I really hope that Apple sticks with their LCD panels, as they are the best LCD panels in the market, and I know what kind of sacrifices they would make if they switched over to OLED (a panel comparable to what is in the Galaxy S5, rather than the amazing ones Samsung is using now).