Perhaps sony means that the bigger chip lets them get more tech in there, but on the surface: a bigger area to fill means you need more light to fill it (unless I missed the current administration cancelling the inverse square law).
If you shine a projector at the wall, the bigger you make the image, the dimmer that image gets.
But the problem remains: using that DSLR for regular shooting may be fine, but when it comes to FX work, often you need a better solution. Even in the film world we use a special stock (different from what they used in principle photog) when doing fx work to reduce grain so we can pull out the details we need. And when budget allows, even a special camera that lets us have a larger film frame, and therefore a smaller grain structure per square inch of image area when transferred to digital.
Then there’s the file fomat the camera spits out. I don’t think the camera noise is killing you (and we have noise killers that can overcome that), its the compression artifacts. When you get right down to it, compression artifacts are little areas of the image that are approximations of what should be there. If you can get that compression “block” small enough you end up with pixels: as close as you can get to an accurate rendering of the original. But as the blocks get bigger (and to keep bandwidth low the blocks are always bigger) they just average what they think is important. And that averaging happens every frame (or worse every, keyframe). The idea is: don’t change the pixels between keyframes if nothing in that area is moving. This is a great way to save drive space but a lousy way to have a clean image. So you end up with details jumping around as the system re averages what its seeing.
Often these cameras will have a digital out: you can plug in your computer or drive and capture or record a higher bandwidth master for VFX work. Even the big sony cameras compress the image to a tape. But the feed off the back is a glorious, nearly uncompressed, 10-16 bit version, far superior to what’s on the tape from the very same camera.
Rule of thumb: don’t digitize after the fact; capture live as uncompressed as you can.