If you want, you can make a few tests and compare the old DOF with the new, and see which one you like more. As an example of the old and new values I’ll quote the hyper focal distance with a 50mm at f/8. (The hyper focal distance is the distance you have to focus at, to get everything from half of the distance till infinity sharp.) The old value (CoC 0,03 mm) was 10,4m, the new one (CoC 0,018 mm) 17,4 m. (If you want to know how to set the hyper focal distance on a lens without a distance scale or with a crippled one: focus on a known distance.)
One final word: with the new table, DOF is even smaller than before. If we also avoid to stop down beyond f/8 and certainly beyond f/11, this means that in practice DOF often will not be sufficient. There is a good solution for this problem however; focus stacking. More about that some other time.
Confusion over circles of confusion (2)
Many pictures are still being printed, though not in the darkroom, but in glossies. The best are often used for spreads in those magazines, so at a size of about A3. Readers however, look at them from the same distance mentioned before, 25 cm (which is a comfortable reading distance if you are young or short sighted or own reading glasses).
Even if you assume the picture editor won't crop your picture, this means that you have to make the old familiar CoC of 0,03 mm 1.7 x smaller. In practice this means that your CoC ends up as 0,018 for 35 mm. (If you would use the 100% view as criterion, you would even end with a CoC of 0,01 mm.)
The new A3/25 cm CoC for 35 mm (0,018 mm) complies also exactly with the maximum resolution for the D700/D3s, so that explains why people with those camera’s didn’t complain that much about the old tables. Of course there was a difference between the sharpness of the camera and the one within your DOF based on the old tables. This difference was 1,7x, a margin that was still acceptable to most.