That’s only true if sensor pixel sizes are the same (which most of the time aren’t).

In general, yes, but not universally - that’s why I say it depends on what you’re shooting. Back to the planetary planetary imaging I mentioned - the planets are so bright in telescopes that you can shoot videos with those tiny pixels. Noise doesn’t matter as you stack/average the images (and here's the big plus of fcamera/RAW - you can get rid of crappy camera NR !). If you used large DSLR pixels, you’d lose details (exacerbated with the bayer layout) and win nothing on noise. On top of that, with a DSLR you’d move a super-large amount of data when in fact you really need just a few thousand pixels per image.

EDIT: But only so we end the digression - yes, from an image quality aspect bigger sensors are preferred unless you KNOW that your particular subject and lighting conditions do not require it (it would be more precise to say - you need the smallest pixels possible that pack sufficient sensitivity to capture a particular image).