With either 120 Hz or 240 Hz, you avoid judder from 2:3 pulldown. Film is 24 fps, and is evenly divisible in either. Not so with 60 Hz, so 24 fps film must be telecined to match, either by the TV or rendered beforehand in software. Digital video shot at 30 fps has no judder. Look up "telecine" if that's not clear. (Let's leave aside the actual numbers as applied to a TV's vertical scan frequency, viz: 23.976, 29.97, 59.94.)
No doubt there are those here who can expound upon the differences between 120 hz and 240 hz display. I'll leave it to them. To me, the absence of judder is the most important thing. I'm unconvinced that a 240 Hz set will be automatically better than a 120 Hz set, but it seems lots of folks think so. Hey, it's more, so it must be better!
As to LED vs LCD, I have one of the former and two of the latter. The LED does not produce nearly as much heat, and supposedly (!) will far outlast the LCD cfl lighting on the LCDs. An edge-lit LED will also typically be much slimmer, and more energy-efficient.
However, since most LEDs are edge-lit, they are prone to uneven backlighting. My own 65" LG 65LW6500 (120 Hz) has it, but it's only noticeable momentarily when changing input. I have a *very* hard time spotting it when actually watching a movie. Read some of the dedicated threads (like the one on the LW6500) and you'll see a number of people have returned their sets because of it. I don't consider it a deal-breaker, but there you are.