As with most anything here, it depends on the specific models being compared.
DVD players in general benefit from having newer DACs and updated disc reading capabilities available for implementation than older CD players. That being said, that does not mean DVD players are always better. The big problem with many DVD players (and especially newer ones and Blu-Ray players) is that the analog stage is mostly an afterthought, which effects the quality of analog sound. That doesn't mean they can't sound better than a CD player still - it's all about the design of the particular models we're comparing. Like many CD players, many DVD players were built to meet a price point and many design features were cheapened out versus the best designs.
Higher end DVD/Blu-Ray players are what really compete with CD players. These usually have well thought out analog stages and are built to appeal to the analog listener, which are often due to the feature of analog multichannel surround outputs. They're often designed to be used as CD, HDCD, SACD, DVD-A, etc. players in addition to playing movies, so they're built with the "audiophile" in mind. Most recently, Oppo was the most high profile player in this market, but there are many others. They also tend to decrease in price more rapidly than CD players due to the "obselete" technology (DVDs), which often makes them a more affordable option than a comparable CD player.
Older CD players were of course built with analog listening in mind. They can have age issues versus newer units, which can effect how well they read and play discs. Many older lasers didn't handle scratches or smudges on discs well, which led to tracking errors (skips and such). While DAC technology has progressed since the golden age of CD players, the early analog stages often were designed to compensate for some of those shortcomings.
Personally, I use a Toshiba SD-9200N, which had a cost of $2k in 2000 as my main CD player. It has the previously mentioned analog multichannel outputs, as well as a dedicated analog stereo output. It plays discs the smoothest and sounds the best of any player I own, thanks to its well thought out design.
As spark1 said, it's all about the circuitry design, and the type of disc read doesn't matter. The best-sounding players will have well-designed analog stages and good circuitry in front of that.
That's a quick rundown of what matters in design. You may find more answers in the "Digital Sources" subforum.
