Well, the 50 f/1.8G hasn't really been released to 3rd parties yet, so it's difficult to say if any of these things are true for sure, but here's a few ways the AF-S version might be better than the AF-D version:

• Autofocus is quieter. This is fairly certain, as the AF-D version made some pretty audible focus noise, but AF-S lenses are all fairly quiet.
• Autofocus is generally faster with AF-S, though the similar 35mm f/1.8 DX AF-S isn't known for lightning-fast autofocus.
• Better image quality, maybe. Again, it's difficult to say at this point, because 3rd party sites like DxOMark and DPReview haven't gotten copies of the new lens yet. Certainly, Nikon is trying to improve image quality, which is why the new version has an aspherical element. The coatings are probably better, as well.
• Autofocus override. You can adjust the focus after autofocus happens simply by turning the focus ring.

Some other differences:

• Different filter size. The AF-S version has 58mm filter threads, compared to 52mm for the older AF-D version.
• Newer lens comes with a bayonet hood and a lens pouch.
• The older, AF-D can go up to f/22, but the newer lens can only go to f/16.
• The AF-S lens is an ounce heavier.
• You can get the older lens today, but you'll have to wait for the AF-S.