large sensors has many effects on photographic quality:
1) Depth of Field
Given when you shoot on a crop sensor using an 50mm lens @ f/1.4, you are still shooting a 50mm f/1.4 lens. Thus, your shallow depth of field (or focus) remains the same at any focal length. However, when you talk about FOV (Field of View), you are talking about "effective focal length", which can sometimes be misled. To better illustrate what I'm talking about, if you take a full 35mm Film SLR, put on a 50 f/1.4, look through the view finder, focus on a relatively close object, you'll notice the shallow depth of field. Take the same lens, put it on a cropped sensor DSLR, and you'll notice the same shallow depth of field, but just smaller spacing around the image (hence "cropped"). So in short, the advantage of a larger sensor is that it will give you more a larger area of the image, thus giving you more of the "shallow Depth of Field" image then a cropped sensor would give. To emulate this "frame" with a cropped sensor, you would have to change lenses, change aperture values, and change your distance from the subject. Thus, people will constantly tell you that a large sensor will give you better "DOF" results, when they really mean it will give you better SHALLOW "DOF" results.
2) Lens Diffraction
Lens diffraction is directly related to the surface area of the sensor size. When the diffraction airy disk become larger than the circle of confusion (which is related to print size/enlargements and sharpness) you loose lens resolution. The best way to see how this works is that think of how big each pixels are inside your "12MP" camera. At a given surface area, you now will have the size of each pixel. When you stop down your aperture, limiting light intensity, your circle of confusion increases. When the circle of confusion reaches the limit of the pixel size, you on at your optimum aperture for maximum sharpness of your lens. Increase the Circle of Confusion more, and you are now diffraction limited, and your images will become soft. Generally, a large sensor will have "bigger pixels" also known as "pixel pitch" or "pixel density" and be less diffraction limited.
3) Dynamic Range
Because we are on a bayer pattern, we have only a single layer filled with pixels sensitive to Red, Green, or Blue. For every red or blue, you'll see 2 green pixels. Because generally speaking (not anymore) Large sensors will have larger pixels, thus, more photon gathering ability (since larger pixels have larger volume). Again this is directly related to pixel density/pixel pitch. Smaller sensors generally have smaller pixels, limiting each pixel's photons. hence, some of the larger sensor cameras will give you better dyamic range (or tone) than a smaller sensor. Because you have more photons within a given pixel, your light signal is much higher, which gives you a higher Signal to Noise Ratio - which translates to a "smoother looking photo." Additionally, this will translate directly to the digital noise, as the less photons you have, the more susceptible you are to digital noise.
What does this mean? Well the newer Full frame cameras, such as the Canon 5D Mark 2 (21.1MP) and the D3X (24MP) has approximately the same light gathering ability as the original 20D/30D (8MP) and the D40X/D60 (10MP) respectively. Because of the newer technologies of the noise reduction software, in theory, if the original 30D/20D has the same Digic4 processor in the body, you should get the same ultra low ISO abilities of the Canon 5D Mark 2. Likely wise on the nikon camp, you should get the approximately same noise free images as D3X for your D40X/D60 cameras should they include the same EXPEED processor.
hope this helps!