The Backlights for LCD displays are white LEDs, which are made by using a Blue LED together with a yellow phosphor to transform some of the light for the Red and Green primaries. The spectrum of an LCD display is just the spectrum of its white LED Backlight filtered through the individual Red, Green and Blue sub-pixel filters within the LCD panel.
OLEDs are emissive devices so their spectra are just the sum of the individual Red, Green and Blue OLED spectra, modified slightly by the touchscreen layer and anti-reflection absorption layer through which their light must pass.
As expected the Galaxy S4 OLED spectrum is relatively narrow with deep notches between the primaries, which results in highly (over) saturated colors, particularly Green in the middle.
The iPhone 5 LCD spectrum is a broader filtered broadband spectrum from the White LEDs.