Canon currently offer two mid-range camera bodies in the form of the 7D and the 5Dmk2.  Both cameras have been on the market for a while, with the 5Dmk2 being the older camera.  The 5Dmk3 has  recently been released but it comes in at a substantially higher price than its predecessor.  It is positioned a little higher in the product line, so at this point in time it is not a direct replacement for the 5Dmk2, which will for now continue to be sold alongside the 5Dmk3 at a reduced price.
Although the Canon 5Dmk2 and the Canon 7D look quite similar, the two bodies are different in many ways, none more so than in their sensor characteristics.
The 7D is an APS-C sensor camera, with 18mp of resolution.
The 5Dmk2 has a full-frame sensor, which is larger than that of the 7D, with 21mp resolution.
There is more to understanding sensor characteristics than just megapixels though, as these two cameras are only 3mp apart when it comes to resolution.
The actual physical size of the APS-C sensor in the 7D is 22.3mm long and 14.9mm high.
In comparison the sensor in the 5Dmk2 is 36mm long and 24mm high.  The sensor in the 5Dmk2 is approximately 1.6x larger than that of the 7D sensor.
Pixels, or photosites, are not all the same, and they have an individual size too, sometimes referred to as pixel pitch.  The 5Dmk2 has fairly large pixels, at 6.4 microns.
The large sensor in the 5Dmk2 is divided up into these photosites, each one around 6.4 microns across, and there are 21 million photosites in all.
The much smaller sensor in the 7D is divided up into photosites, each one around 4.3 microns across.  There are 18 million photosites/pixels in all.
It should be clear from following this explanation that the photosites or pixels on the 7D sensor are much smaller than those of the 5D sensor.
Looked at another way, if you took the larger pixels of the 5Dmk2, and divided up a 7D-sized sensor using these pixels, you would only get 8 million of them to fit on it (which would equate to the 30D sensor of a few years ago).
When comparing the full frame 5Dmk2 image with that of the APS-C sensor of the 7D, bear in mind that the sensor cannot change the focal length of the lens.
Those in the market for a mid-range Canon dslr body often end up having to choose between these two camera bodies, and as such it is useful to be able to see and compare images taken with the two cameras, side by side.
With the help of Chris Frylink and his 7D, we set up the two cameras to shoot some comparative images.
We used a Canon EF 70-200 f/2.8L IS II lens, mounted on a tripod.  Only the camera body was changed each time.  No sharpening was applied other than a default setting of 25 in Adobe Camera Raw.  Raw images opened in Photoshop CS5, downsized and saved using File Save For Web and Devices at 190kb file size.
For this comparison, in order to make up for the difference in subject size due to the viewfinder crop, we set the focal length of the zoom lens at 160mm when shooting the 5Dmk2, and at 100mm for the 7D.  This gave us a similar size subject in each frame.
Canon 5Dmk2, focal length 160mm, 21mp, no cropping, iso 400, f/5.6.
Canon 7D, focal length 102mm, 18mp, no cropping, iso 400, f/5.6.
The lens projects the image that it captures onto the camera sensor.
The larger sensor of the 5Dmk2 captures 36mm x 24mm of what the lens projects which is pretty much corner to corner of the image circle.  The smaller 7D sensor captures the middle portion of that, with its 22.3mm x 14.9mm sensor.  So a portion of what the lens projects does not get recorded on the 7D sensor, that being the outside edges of the frame.
By zooming in from 100mm for the 7D shot to 160mm for the 5Dmk2 shot, the subjects ended up the same size, as shown above.  There is no cropping with the above two images.  As these images are taken at iso 400, and downsized to 800×533 for web use, it is difficult to be able to evaluate any quality differences at this point.  Comparing the two full-sized images on my monitor showed little difference in image quality at iso 400, although the 5Dmk2 image had a slightly smoother feel in the light toned out-of-focus areas of the background to my eye.
For the next pair of images, we shot at iso 800 and cropped heavily in order to make it easier to evaluate quality on the downsized-for-web pictures.
Canon 5Dmk2, focal length 160mm, cropped to approx 3mp, iso 800, f/5.6.
Canon 7D, focal length 102mm, cropped to approx 3mp, iso 800, f/5.6.
At iso 800, it becomes clear that noise is a little more visible in the 7D image, particularly in the out-of-focus background areas.
It is important to take note of how the noise is most visible in areas of smooth or similar tones, like the dark background area, and the light-coloured wall.  The noise is not nearly as noticeable in the heavily textured fur and busy tones that make up the bulk of the subject, the baboon.
Also bear in mind when evaluating these two images that the 5Dmk2 image has a shallower depth of field, due to the longer focal length we used to equalize subject size.  This can be seen in the fur on the side of the baboons face.  On the 5Dmk2 image, this fur is more blurred than on the 7D, due to the shallower depth of field resulting from 160mm of focal length compared to 100mm.  It is important to remember that this means that larger portions of the 5Dmk2 image are out-of-focus.  However, both images were taken at f/5.6, and both are pretty sharp on the baboon’s eye, where the AF point was positioned.
The next pair of images were taken at iso 1600 and again cropped heavily.
Canon 5Dmk2, focal length 160mm, cropped to approx 3mp, iso 1600, f/5.6.
Canon 7D, focal length 102mm, cropped to approx 3mp, iso 1600, f/5.6
After extensive use of both of these camera bodies, my own findings in actual shooting conditions supported our findings here.
When you are able to get enough pixels on the subject, or enough focal length on the 5Dmk2’s full-frame sensor, in order to make up for the smaller sensor on the 7D and it’s consequent 1.6x field-of-view crop, then it offers superior image quality to the 7D.  Although there is a difference in image quality at low iso sensitivity settings, it only really becomes noticeable from iso 400 upwards.  At iso 400, both cameras are able to produce clean images for print though.  The real difference becomes significant from settings of iso 800 and upwards.  At 1600 iso the 5D mk2 is perhaps close to one stop cleaner than the 7D.  Of course, one can only enjoy this advantage if you are able to make up the difference in subject size between the two cameras, either by moving closer to the subject, or by using a lens with a longer focal length on the 5Dmk2.
Both cameras can take usable images at iso 800 and upwards, but the 5Dmk2 images are cleaner, and will need less processing work.  The 7D images taken at iso1600 and higher iso settings will benefit from some careful processing work to extract the best from them, and perhaps reduce some of the noise.
We did not calibrate the two camera bodies this the lens.  Whilst there were no clouds in the sky, and we shot as quickly as possible between changing bodies, there might be slight changes in the available light.

For my purposes, in raw format, I felt completely happy that the pictures were sharp enough and that both lens and camera combinations were working properly.
With proper sharpening applied, there would be lots more detail showing on the subject.  It is also important to remember that the only sharpening applied to these images was the Default Amount of 25, which is a low amount, from the Detail panel in Adobe Camera Raw.
Sharpening and adding contrast to the entire image would lead to noise becoming more pronounced due to the sharpening acting on the noise detail.  If your own images show much higher levels of noise, check to see if you are not adding sharpening and contrast to the parts of the picture where noise is present.  Also remember that heavy cropping will tend to make noise more visible, specially in background areas that are low in contrast.

Look through the blog archives in order to locate other comparison posts where different Canon lenses and cameras are compared.