Alright, I just tried the sony 720p preset you said, and also tried exporting via File > Export > Adobe Media Encoder.
I selected Quicktime > H.624. Settings wise I selected:
Frame Size: 1280×720
Quality: 100
FPS: 59.94
Field Order: None Progressive
Pixel Aspect Ratio: Square Pixels (1,0)
Bit Depth: 24-bit (wont allow me to change)
Bitrate: 5.24
I still get bad quality compared to my original. I have bad pixelation of the video even at 100 quality.