Looking at the picture you'll notice a series of borders. The blue border represents what the picture would look like if taken on a FF camera (my 5D). The red border represents what the picture would look like if you took it using a 1.3 crop factor (1D Mark III). The yellow border represents a 1.5 crop factor found on some Nikon cameras which I believe is called a DX sensor. Finally the green border represents what the picture would look like if taken with a 1.6 crop factor (Rebel series, XXD series, 7D). Is one crop factor better than the others? No, not in my opinion they aren't, they're just different. Supposed you wanted to achieve the look of the 1.6 crop factor with your FF camera, how would you do that? Depending on the lens mounted you could either zoom in on the subject or if you're a prime lens you can use foot zoom -- take a couple of steps closer to your subject.
Although I really like the image above to show the difference is the various crop factors it's hard for me to visualize the difference between a FF and 1.6x crop factor because I can still see the extra pixels even when I'm looking at the 1.6x crop factor area. Below is a series of three photos I took in our back yard. I used my 5D, the rented 1D Mark III and my 40D to take the same shot. Used the same lens on all 3 cameras and set it as close as I could to 28mm. Looking at these images you can clearly see the differences between the three crop factors.
5D @ 28MM
Notice how you can see the concerete pad and all of the pine trees across the street.
1D Mark III @ 28MM
Notice how you can only see a little bit of the concrete pad and the tops of the trees are chopped off, but notice how much closer the fence appears to be compared to the photo above.
40D @ 28MM
Notice how you can't see any of the concrete pad and more of the trees are chopped off, but again, notice how much closer the fence appears to be compared to the above photos. This is one reason why sports photographers like cameras with a crop factor. It gues us additional reach which is very handy when you're stuck behind a fence or can't shoot from the side lines.
If you're interested in seeing shots at 17, 24, 28, 35 and 40MM with these three cameras check out this Crop Factor Testing Set on my flickr photo stream.