Noise is decided by the quality of the sensor, and the solid angle of light that hits each point on the sensor. The solid angle as it happens also decides depth of field.
So it is always true that you should apply crop factor to aperture. ISO is just not the correct factor to describe gain because an inverse crop factor is applied to it in effect.
So at the same exposure and shutter speed, at f/3.4 on FF you will get the same image with the same amount of noise as you would at f/1.7 on M4/3.
I'm interested to learn more about the effect of light angle on noise. Do you have a source that talks about this? I didn't find anything useful in 2 minutes of searching the web.
As for light angle, it's a consequence of the second law of thermodynamics, that translates in optics as the conservation of étendue.
Basically what this means it that the amount of light captured from a light source is equivalent to the solid angle of light from that light source onto the entrance pupil - whose size is the focal length divided by the f number.
So basically, what determines in the same scene how much light is received by the sensor depends on the size of the aperture in milimiters.
So on a sensor of the same efficiency, it's the physical size of the aperture that determines how much light is captured.
> what determines in the same scene how much light is received by the sensor depends on the size of the aperture in milimiters
That's true, but the amount of light is not the intensity of light.
Yes, you will need four times the ISO. But you will get exactly the same amount of noise.
For 150g on full-frame you can get a 50mm 1.8, at a cost of 150$ brand new. So on full frame at a similar weight and at the same price you get superior optics.
If you really care about the weight, the 40mm 2.8 has the same weight and the same price but superior optics again.
All modern FF cameras do distortion correction too. M4/3 lenses are not especially decided to trade-off distortion for sharpness anymore than full-frame.