I would say the nod to the best overall 2D picture quality (between the Panasonic and JVC) goes to the JVC. Two different technologies... Primarily the JVC doesn't rely on an auto iris and has much better blacks.
The Sony 50 and JVC are more comparable in tat department... The Sony probably has better 3D capabilities and the JVC has an advantage because of auto memory zoom (if you have a 2.40:1 screen you'll want this). JVC also has created the 4k eshift technology that is on the 35.
Bottom line, you get in this price range and the projectors are all really nice. If I were you, I'd make a list of the things that are most important to you (lumens, 2D capability, 3D capability, motion modes, lens memory, etc) and read professional reviews (projectorreviews and projector central are decent starting points).
I ended up with my JVC because I did my own head-to-head, JVC vs Panny, in my theater room. The JVC won out for my needs. Your needs/wants may differ, tho.