In low light, the larger sensor shows less noise, so it is iso performance, right? Wrong.
The iso performance of a sensor is measured for the full sensor area. Other things being equal, a sensor with higher resolution has more noise per pixel but since each pixel – hence, its contribution to noise – is smaller, not more noise overall. For an iso rating of a sensor, the single pixel does not count, the whole image counts.
Other things being equal again, iso 100 on a fullframe sensor looks better than iso 100 on a crop sensor. So far it looks reasonable: Larger sensors = less noise. But if you use a lens on each camera yielding the same field of view and depth of field, you have to use longer focal lengths on the larger sensor and thus stop down further on the larger sensor to keep the same depth of field. In low light, when iso is above the camera’s base iso, you have to use a higher iso value to compensate. It still looks as good as the lower iso value on the crop sensor. But you don’t have an iso advantage in terms of lower noise on the larger sensor in this situation.
Let’s go deeper. If the fullframe user uses the lower f-stop, too, but also the smaller focal length like on the crop sensor, and crops the image in post to get the same field of view, the remaining image pixels get enlarged and so the noise gets amplified as well. Still no noise advantage!
The only option to get less noise with the larger sensor is if you can live with a shallower depth of field.
Again, a fullframe sensor only gets you less noise if you can live with a shallow depth of field, or if you are at very low iso values already. In the latter case, today’s crop sensors are quite good though, more quality is usually not needed for an amateur.
Is sensor size useless then? Of course not
Other things being equal, optical issues of a lens have a certain extent. The larger the sensor, the smaller the the lens issue compared to the final image. Meaning you get more undistorted image information just through the larger sensor area.
On top of that, with the larger area you use longer focal lengths and stop down further to get some depth of field. Stopped down a bit (but not too much) the lens performance will improve, getting you even higher resolution. That is the real advantage of fullframe versus crop! You get your lenses more often to the peak performance, and the larger area captures more information even if you shoot wide open.
Another reason for fullframe: At least in the Nikon world you get the best lenses here. The DX range consists mostly of consumer-grade products, and while you can mount FX lenses on a DX camera, you cannot fully use their performance with a crop sensor. I am told it is different in the Fujifilm world where a lot of APS-C lenses are made to professional standards.
Do you need fullframe? I personally look for a reason to finally give in. But honestly? 1.5x crop is just some stop in terms of light and thus iso performance. Meaning yes it can be noticeable if you look at individual pixels – but since when has a good photograph to be be pixel perfect? If you think it does, why being satisfied with “full”frame, which in film terms is amateurish small frame? Why not a larger sensor? Such cameras are available, look at Pentax and Fujifilm …
Conclusion
I am a crop-sensor user but of course admit that systems with larger sensors can offer better technical quality. But the common idea that this advantage would be less noise in low light only applies to situations where not a lot of depth of field is required.