The difference is the level of processing done with the data.
Level I data is raw radar data (you don't want to see that stuff).
Level II is the radar data after a small amount of initial processing. Level II data only consists of Base Reflectivity (0.5 dBz increments), Radial Velocity (1kt increments), and Spectrum Width. The radial resolution of the velocity product is 250m. In terms of vertical resolution, there are typical 9-14 vertical tilts availab.e
Level III data is formerly known as NIDS data... More processing has been done with this data. This means that more products are available, but at a lower resolution (than Level II). Products include Base Reflectivity (5 dBz increments), Radial Velocity (5kt increments), Storm-Relative Radial Velocity (5kt increments), Echo Tops, Vertically Integrated Liquid (VIL), 1hr/3hr/Storm total precipitation estimates, and the Vertical Azimuth Display (VAD) wind profile. The radial resolution of the velocity products is 1km. In terms of vertical resolution, only 4 tilts are available.
So, not only are the increments smaller (higher resolution) for Level II data versus Level III (NIDS) data, but the spatial resolution (horizontal and vertical) is greater as well. For example, for the velocity products, there is less averaging for the Level II data than for the Level III data. For a very quick example of the two, head on over to
http://nexrad.allisonhouse.com/faq/2v3/ for a look at the 5-9-03 OKC Supercell with Level II and Level III radar imagery.
There is a good PowerPoint presentation regarding the benefits of Level II radar imagery versus Level III, but I can't find it at the moment. I thought it was on the NSSL or OU domain...