I'm super interested in this as well. I have had a hard time with newer TV's. I had a Samsung 46" 1080p LCD (CCFL lit) from 2008/2009 that was quite good (60hz, 300 series, really basic TV). I got a 2012-2013 model CCFL Toshiba (720p) 32", which I quickly got used to.
I've never had a problem with Plasmas (unless the source was bad, a la bad FRC/Temporal) but I got a newer LCD (LG, 2012 model, 120hz, 43") and it was TERRIBLE. Instant headaches after a minute.
My girlfriend has a 2014-model Toshiba 40", it was fine even though LED backlit.
So I grabbed a brand new Toshiba 1080p LED from Best Buy. It's ... ok. Not great, not as good as the others, but tolerable. I'd love to say I loved it, but I just don't. I tolerate it.
I'd love to know which new TV's are better than just "tolerable" and are actually "good". What does everyone here use that isn't a Plasma?
My primary TV, by the way, is a 60" LG Plasma (final model before they stopped producing Plasmas last year).