Actually, when you take noise into effect, you also have to decrease the effective aperture to get a valid comparison with a larger format. I can't do the math, but it's also roughly a stop.
That is, f/1.3 @ ISO 100 on APS-C really is comparable to f/2.0 @ ISO 200 on full frame. And f/1.3 @ ISO 100 on full frame would be comparable to f/1.0 @ ISO 50 on APS-C. (Roughly, with rounding, etc., etc., etc.)
So the noise from a EOS D30 (2001) is one stop behind the 1D X? I don't think so. Everyone understands noise is in constant flux throughout models, formats, etc. So I think it is fair to leave noise out of the equation as it is not a constant like shutter speed and aperture. Given two models of camera it is fair to make a comparison on the level of noise and how many stops of advantage one has over another, but to make a blanket statement is not fair.
Here's the math:
FF crop factor: 1
APS-C crop factor: 1.6
f/1.3 * 1.6 = f/2.0 equivalent 90mm (for background blur of 55mm f/1.3 lens in FF terms)
f/1.3 / 1.6 = f/0.83 equivalent (although your point is misleading as an EF-M lens has a flange distance too short for a FF DSLR - and most likely an image circle to small to cover a full frame sensor)
All you need to do is multiply the aperture (or focal length) by the crop factor to go up in formats, and divide to go down.