There was a rumor about the iPhone having an OLED screen back in the day, but nothing been heard since. The advantages over LCD would be, better battery life, thinner/lighter, better refresh rate, and MUCH higher quality colors.
The disadvantages are price, resolution, and lifespan. Unfortunately, OLED is still new, thus expensive technology, and that 11 inch TV Sony sells only has a resolution of 960 x 540. The lifespan isn't really that bad, for Sony's *production* OLED TV (the 11 inch one that costs $2500), Sony claims 30,000 hours to lose half the brightness. Now, a separate company claims only 17,000 hours, but they only tested 1000 hours and based their results on that. But even if that's true, you could be actively using your OLED iPhone for 8 hours a day for more than 5 years before the screen was half as bright. Of course by then you'll need to send your phone in for a new battery anyways...