I have an LG 65" 65LW6500. I confess I don't use the 2D -> 3D conversion very often. Oh, it does a creditable job of it, but doesn't compare to a well-done 3D movie (like Hugo!). One *shot* in 3D, mind you; 3D done in post falls somewhere in between. Like John Carter.
Anyway, conversion gives the illusion of a little depth. Funny that The Phantom Menace was mentioned earlier in the thread. That one looks rather good when converted. OTOH, I felt certain that The Searchers (1955) in VistaVision, would look good converted. It doesn't. Then there are the occasional weird artifacts. Has anyone else tried the coronation scene in ROTK? It looks for a split second like Aragorn's head is disembodied, the silk neck wrapping being pushed into the background. Might just be my eyes, I dunno.
What I'm getting at is that how good the conversion looks will depend on the source material. The conversion uses sophisticated algorithms to make a best guess as to what is in the foreground, background, etc., and adjust accordingly. Some movies will look a lot better than others.