Plasmas have fallen out of favor. But that means the remaining companies making them (LG, Samsung) have the market to themselves. Larger plasma TVs are lower priced then comparable LCD sets.
LED backlit sets have the ability to have local dimming.
There are flavors of LED sets (edge lit, full array).
Plasma sets will always have a reflective front, whereas LCD sets can have a mat finish screen.
I personally prefer LCD/LED TVs as they are easier to diagnose and fix compared to plasma. I think most of the picture difference can be measured in a lab, but probably won't be as evident in a home environment. Especially since the source is often no optimal.
If you want larger then a 65" set (barring outrageously priced niche sets), you are looking at a LCD set (70", 80", 90").