Since you have a plasma, i presume your display is 40 inches or higher, and lets presume your plasma is actually HD resolution, then i'd definetly go buy the HD DVD addon drive.
As for the differences.
Standard DVD is approx 720x480 pixels of resolution.
HD DVD has 1920x1080 pixels of resolution.
When you upscale DVD all your doing is making the pixels larger. ie a 1x1 pixel becomes a 2x2 pixel.
Now the 2x2 pixel = 4 total pixels but it only contains one pixel of colour (as is is based on the information contained on the DVD).
For HD DVD that same 2x2 pixel area will contain 4 pixels of distinct colour information (instead of the 1 pixel; of information on DVD) meaning you get more information which equals beter visual clarity.
Note HDDVD is more like 5x the visual information, but abreviated to 4x to make the example clearer.