It appears that this discussion is taking off into a somewhat different direction than the OP had intended... But talking about noise performance on different (size) sensors is also interesting, even if a bit off-topic.
Now, I am not an expert in any of this, but reading the last few posts makes quite obvious that few, if any, of the last posters are, either. Just a few points/thoughts:
First: an APS-C sensor is smaller than a FF sensor, and thus a lower amount of light hits the total sensor surface. However, the framing is also different, and the image from the APS-C sensor has exactly the same size on the FF sensor because that is defined by the lens, not the sensor. Consequently, the amount of light per unit surface is the same on both sensors, and the noise performance can not depend on the sensor size.
Second: Noise comes from the physical, chemical, and electrical properties of the sensor - or of each individual pixel, to be more specific. A photon hitting a section in the CMOS-chip promotes an electron to the conduction band, thus leading to a measurable current. Occasionally some other effect leads to current, producing dark counts. The current that is collected from the chip needs to be amplified, and the degree of amplification is set (in a camera) by the ISO speed. The amount of dark counts remains the same, but if pictures are taken in low light then the ratio between dark counts and "real counts" gets worse. Since the amplification process does not distinguish between the two types of currents, high ISO leads to more noise. The number of dark counts can either be constant for any single pixel, or a constant of the surface. I personally don't know which one it is, but they lead to different results if we then compare different sensors.
If we have a constant number of dark counts per pixel, then obviously we get lower noise in low-MP sensors of a given size) since there the amount of photons hitting each pixel is larger (as the pixels are larger), and the ratio of good/bad electrons is better. In the extreme case of one single pixel we would have the lowest absolute rate of dark counts, and thus the highest IQ (OK, the term "image" becomes questionable here...)...
On the other hand, if the rate of dark counts is a function of the total surface (and does not depend on the number of "cuts", or pixels, we make into that surface), then the number of MP will not matter. We then get lower dark count rates per pixel for higher MP, but the summed rate is still the same.
As far as I understood it so far, the fact that in general FF cameras have lower noise is mainly due to the fact that the sensors are the most recent types that have been developed. I have no experience with most models that are out there, but I would think that newer crop sensors will give lower noise than older FF sensors - simply because they are newer. Any attempt to quantify high-ISO performance simply on size and MP-count alone don't work because no two sensors of different size are the same otherwise.
I am open to hearing that all I have just written is nonsense... But what I would really like to hear is what a real expert has to say. Someone who builds the sensors, or who does research in that field...