DME is used alone without other sugar, and, honestly, it doesn't make any difference. Some people are purists and think that a little sugar will harm their beer. It just aint so. In my experience, corn sugar is a much faster, cleaner priming sugar and contributes zero taste to the beer in the quantities used for priming. DME will definitely take longer to condition and you use a bit more of it usually. So, no real difference except corn sugar works better for the purpose.
From what I understand about it, when using DME, the yeast doesn't require oxygen to convert the sugars to CO2 or alcohol, which is why it takes so much longer. When using corn sugar or cane sugar, the yeast uses oxygen to convert everything and doesn't take as long. Like Janx stated, I can't really taste a difference between the three. I've used DME, corn sugar and cane sugar and I've never been able to taste a difference.
I've been using DME since about my third batch. I just like the 'purist' aspect of it. You do need more (1-1/4 cup) and I guess it does take a bit longer to carbonate. I haven't used corn sugar in so long, I wouldn't know for sure!