Doubling the focal length does make a lot of difference to the depth of field. I am no expert in this area and may have it wrong. But, my understanding is the depth of field, all else being equal, increases linearly with f-number but decreases inversely with the focal length squared. So, if you double the focal length of the lens, the dof decreases by a factor of 4. Shooting a 1000mm lens at f/10 gives the same depth of field and subject separation as shooting a 500mm lens at f/2.5. Similarly, shooting a 400mm at f/5.6 gives the same depth of field as shooting a 500mm lens at f/8.75. But, it gets more complicated if you crop the shorter focal length image and view at the same size as for the longer. I think you then have to divide the dof by the crop factor. So, after cropping, the 1000mm lens at f/10 will give the dof of the 500mm shot at f/5. And the 500mm at f/7.1 will give the very close to the same dof and subject separation as a 400mm at f/5.6.

**Take home message is that the 500mm/7.1 gives us croppers the same subject separation from background as a 400/5.6.** Please correct me if I am wrong.

Edit SecureGSM posted just as I was posting and so it seems my maths is correct.