LEDs in general allow for thinner, less power-hungry displays. The edge lit LED units are currently the thinnest of all displays, 'cuz the LEDs are on the edge, not behind ;-)
Back lit displays have the possibility of doing what's called "local dimming", meaning that they can dynamically lower their brightness when a portion of a scene is dark, thereby giving the impression of deeper blacks and higher contrast. I've seen mixed reviews on whether this is really a big advantage or not, so . . .
Now, just because a TV has LED backlights doesn't mean it has local dimming - you have to look specifically for that term or some other vendor-specific term meaning the same thing (check their websites).
My personal opinion is that it doesn't make a lot of difference - other issues like does the unit have some kind of anti-reflection coating, and how bright is the room you're watching in, make more difference.
Read online reviews for the units you're interested in, and watch for what people are complaining about, and try to be honest with yourself about what really bugs you and what doesn't. Hope this helps.