There are just two differences: The new Superdrives write DVD-Rs faster (8x instead of 4x) and they are capable of burning double-layer DVDs. For the near future, the faster DVD write speed will be more beneficial. 8x media is almost as cheap as 4x media today and it'll be nice to burn DVDs a little faster than before.
In the long run, though, it'll be nice to have double layer capability. Right now the discs are extremely expensive, but eventually they will be more cheaply available. Basically, a double layer disc lets you store twice as much data. This also lets you copy the entire contents of a video DVD to a single burnable DVD. Video DVDs have been using double layer technology for a long time, so they can hold 8.8 GB as opposed to 4.4 GB. With a standard DVD-R, you had to compress the video in order for it to fit.