What software is being used for the playback makes a huge huge difference.
The big thing to remember is that DVD's are encoded at (for PAL) normally intended to display on a TV that does 625 lines interlaced (alternate lines refreshing), with CRT's also "blurring" it a bit - if the DVD is an NTSC encoded one it'll look even worse due to the lower res of NTSC.
A PC monitor, even an old CRT PC momitor will be running at several times that resolution, refreshing the whole image at least 60 times a second.
Basically the PC display will tend to show up every fault with the encode/source material much more than a DVD player connected to a CRT TV.
Good PC DVD playback software will have varous filters it'll apply to help it cope with those issues, and allow for better scaling (it's sometimes interesting to see how the same bit of material is handled by 3 or 4 different "media" players on the PC, I use Mediacetnre classic, Zoom Player and VLC on a regular basis and the same video can look very different on each).