If the TV is on its table stand, it usually doesn't matter how thick the panel is other than the LED is a little lighter in weight for moving it.
Where an ultra-thin panel is advantageous is when wall mounted to make it appear more like a painting hanging on the wall.
A thicker panel however can offer more room for better internal speakers - an advantage.
Along with older CCFL backlit LCD sets, Samsung has some new cheaper LED models (the EH series) that has fewer rear backlit LEDs instead of the more expensive edge-lite LED models (ES series). The EH LED models are thicker panels like the older CCFL LCD models too.
Having backlights in the rear (CCFL LCDs and some of the cheaper LEDs from Samsung - the EH series) offers less of the flashlighting and clouding effects visible on some very dark/black scenes - another advantage.
Unfortunately the cheaper CCFL LCDs and EH LED models don't offer the high end features the thin edge-lit LED models do, such as Smart TV with 3D and extra HDMI ports.
For example the highest end EH model Samsung has out is the EH6070 that offers 3D but no Smart TV (internet apps) and only 2 HDMI ports.