From the DisplayMate 6+ review:
"Current LCD Strengths: higher Peak Brightness with high Average Picture Levels, no Peak Brightness variation with Average Picture Level, wide Color Gamuts with Quantum Dots, smaller Color Shifts with Viewing Angle, higher power efficiency with high Average Picture Levels, and much higher worldwide market share.
Current OLED Strengths: higher Peak Brightness with lower Average Picture Levels, easier to increase screen resolution and ppi, perfect Blacks and infinite Contrast Ratios, wide Color Gamuts, smaller Brightness shifts with Viewing Angle, better Screen Uniformity, faster Response Times and no display motion blur, higher power efficiency with lower Average Picture Levels."
Yes that's the general truth when comparing MOST LCD and OLED displays but not when you compare the specific one in the Note 4 with the one in the iPhone 6. That's not fair to compare a general overview of screen technology when were talking about 2 specific displays.
Also some of those strengths listed have nothing to do with image quality, like market share and power consumption.