When I watch my videos from my sonya6000 on Sony PlayMemories, the quality is noticably better than when I have those videos finally uploaded them to my computer and rewrap them in a .mov file using ffmpeg. Why is this?
This could be because QT is interpreting the video as if it were in video levels (16-235) and sony consumer cameras (at least the N5 and the A5100) record in weird levels (16-255).
I have not found any software that accommodates this properly (I guess playmemories, being a sony product does), and usually manually configure the software to interpret the footage as data levels (0-255) and then lower the shadows. It is not perfect, but it is as good as it has gotten for me.
It's probably because of the re-wrap. Something is going wrong there. Do you really need to do a re-wrap?
The 16-235 issue can be a problem as well. With my NEX-5N, even without a re-wrap, I always had to bring down the white point in Premiere to restore the highlights.