The quality of audio output varies among different CD players, but the range is nothing compared to DVDs. Moreover, the quality gap isn't always determined by how much you pay. What it all comes down to are two key electronic components that largely determine the value of your DVD player.
Indeed, it's not outputs, the DAC (digital-to-analog converter), formats supported or add-on features. And it certainly isn't the brand name. What you really seek in a DVD player is accuracy of the video image, and that's hard to find by just looking for a particular brand. Film audio makes a few compromises from natural sound, but nowhere near what video has to make. Think about this: 35mm film has a resolution of 4096x4096 pixels, compared to 1920x1080 for high definition TV and 720x480 for DVD.
So even though DVD looks beautiful, compared to the 35mm film used to shoot the movie, DVD video is very dumbed down from the original source material. Audio has its compromises, to be sure; Dolby Digital 5.1 audio uses a compression ratio of around 15:1, but the loss off information is nowhere near as great as compressing video from 4k to 480.