viewing angle has little to do with the backlighting method.
LED backlighting uses about 20% less power than CFL.
The advantage of LED backlighting is that it can be turned on and off by pixels or blocks, which increases the black level...or better said, decreases the light level coming through.
Most of your mid to low end LED TV's use zone blackouts. Meaning the screen is divided up into blocks and when that part of the picture is black or mostly black, it turns off that section. Typically these sets the LED backlighting is almost always on because rarely do you have wide coverage of black. The cheapest sets that use LED backlighting usually just have always on LEDs with diffusers in front to spread it out.
The highest quality (and typically most expensive) will have variable LED backlighting per 3 pixels. 3 pixels = RGB. Furthermore, the LED backlight is not just on or off, but will also vary in intensity.
The thickness of the TV really doesn't have much to do with the backlighting or LCD technology. Making the plates thinner and getting rid of or spreading out the electronics behind the screen is what makes that possible.
Recommendation? What fits your budget and the spot you want to put it.