A scratch will be worse on a DVD than on a CD because of higher storage density and because video is heavily compressed.
DVD error correction is at least ten times better than CD-ROM error correction and more than makes up for the density increase. It's also important to realize that MPEG-2 and Dolby Digital compression are partly based on removal or reduction of imperceptible information, so decompression doesn't expand the data as much as might be assumed.
Major scratches may cause uncorrectable errors that will produce an I/O error on a computer or show up as a momentary glitch in DVD-Video picture. Sometimes the smallest scratches can cause the worst errors (because of the particular orientation and refraction of the scratch). There are many schemes for concealing errors in MPEG video, which may be used in future players.
See How should I clean and care for DVDs? for information on care and cleaning of DVDs.