That depends on what kind of player you buy. If you buy a $200 DVD player you probably have a CD player that is comparable to a $100 unit. If you buy a $1000 DVD player, it should be much better but not as good as a $1000 CD player. I have a nice Marantz special edition player that I use for music, because my DVD player is a cheap unit.
None of this takes into effect DVD audio and SACD's