It depends on the display type. Some displays emit energy based on the intensity of the image (CRT, Plasma).
Others always generate light but then mask out the light with a matrix display which typically has a pretty constant energy usage (LCD, Projection). Still others only require energy only when they change (eInk, future color pigmentation eInk variations).
And of course power variations in each technology, FL LCD v LED LCD. Older Plasma displays vs newer Plasma displays. The size of the display, (your 52" TV v 3" cellphone)
For CRT/Plasma there is also refresh rate to consider...
While it generally isn't true of computer displays, some LCD televisions do have slightly reduced power consumption on black. It's not from the LCD shuttering the light from the backlight, but from control electronics reducing the backlight brightness dynamically. Those "dynamic" contrast specifications on some displays are a little misleading.
One tends to think of a display having a high contrast figure as being more effective at blocking the light when displaying black (less "Bleed-through"), but they cheat by dimming the backlight.
That may result in small bright areas in dark scenes ending up a bit darker than they should be.
With all backlit LCDs, lowering the (backlight) brightness setting conserves more energy than having the content dim the same amount. Using the lowest acceptable brightness setting not only saves energy, but extends display life.
C.R.T.s usually have the greatest change in power consumption with content brightness shifts, particularly in Trinitron tubes.
And of course power variations in each technology, FL LCD v LED LCD. Older Plasma displays vs newer Plasma displays. The size of the display, (your 52" TV v 3" cellphone)
For CRT/Plasma there is also refresh rate to consider...
etc etc etc.