Below are some examples comparing Nikon D3 + Nikkor 14-24mm lens with Nikon D200 + Nikkor 12-24mm DX lens. The Nikkor 12-24mm DX lens was built solely for Nikon DX SLR cameras (the smaller sensors). This is a smaller lens, and it will only project to DX size sensors. Now, a DX lens will still work on an FX digital camera, like the D3, but it severely limits the capability of using an FX camera.
All the images below are 15% of the full size, embedded JPEG file from the RAW (using DCRaw to retrieve the JPEG)
Nikon D3 with Nikkor 14-24mm f/2.8 lens @ 14mm. 1/640s, f/8, ISO 250, focal length 14mm
Nikon D200 with Nikkor 12-24mm f/4 DX lens @ 12mm. 1/640s, f/8, ISO 250, virtual focal length 12×1.5=18mm
Nikon D3 with Nikkor 14-24mm f/2.8 lens @ 14mm, but this time I set the D3 to capture in DX sensor size, effectively turning the D3 into a ~6 megapixel camera.
1/640s, f/8, ISO 250, virtual focal length 14×1.5 = 21mm
Now, here is what a DX lens (the 12-24mm f/4 in this example) would look like when used on an FX camera (Nikon D3 in this example) in FX mode!
To spin this another way — You would need a ~9.2-16mm on a DX camera to replicate the angles of view that this 14-24mm lens gives on FX and film cameras.