Since Dave brings up the theoretical limits of a 1/2.3" sensor, I thought I'd look at noise levels of compact cameras. The DxO Mark website has analyzed the Nikon P6000, which should be using sensor technology comparable to the D90 and D700.
Using
this calculator, I figure that the 1/1.72" sensor on the P6000 is about 4.5 stops different from a 135-size sensor. That is, with 21mm at f/3.3, a 1/1.72" sensor has a comparable FOV and DOF to 100mm at f/16 on a 135-size sensor.
At ISO 64, the P6000 has a SNR of 29.2 dB; at ISO 1600, the D700 has a SNR of 30.7 dB. At ISO 400, the P6000 has 20.9 dB; at 12800, the D700 has 21 dB. That's about 4.5 stops of difference at a given noise level. So you could claim that there is no noise benefit to the D700 over the P6000. (The DxO measured ISOs come out at about 4.5 stops, too.) The DxO chart can be seen
here.
Dave has a valid point, that larger sensors have a higher theoretical signal-to-noise limits. However, I think Haakan's point needs to be taken to heart: with current technology, larger sensors capturing the same image will have no less noise. (This assumes that we can extrapolate Nikon's sensor technology to other brands.) In the future, larger sensors probably will produce lower noise in the same image, but technology hasn't reached that point yet.
The noise-related benefit of larger formats, then, may be stated as not having fast-enough lenses for smaller formats. An image produced by a lens at f/2.8 on a 135-size camera would require an f/0.5 lens on a 1/2.3" camera--without such a lens, the smaller sensor cannot produce a comparable image. (Or, a lens at f/5.6 on a 4x5 camera would require f/1.8 on a 135-size camera.) But with such a lens, on similar-technology sensors, the noise results would be about the same. Buying a 200mm/2.8 for your APS-C-size camera probably makes more sense than buying a 300mm/4 and a 135-size camera.
Alternately, if you desire (or are willing to have) a shallower depth of field than the available lenses for smaller sensors permit, larger sensors will have less noise. But using a different DOF will capture a different image, and Haakan reasonably wants to compare images with the same optical attributes.
You can also improve noise by moving to a newer sensor technology: the P6000 is only 4 stops behind the D3, which is to say that the P6000 has about one-half stop less noise than the D3 when using the same DOF. See
here. Likewise, the D90 appears to be about 1 stop better than the K20D,
see here.
The upshot, I think, is that 135-size cameras are not improved APS-C-size cameras--nor are SLRs improved compact cameras. They are different formats with tradeoffs aside from cost, size, and weight. Moving to a larger format will not necessarily reduce the noise in your images.