It's all a matter of taste. I ferment it to completion (around 0.996), carb it like beer, and I like it that way. Any sweeter and I would not like it.
If you recall:
My girl likes cider, are there any simple cider recipies?
This is for his chick, so I doubt the cider referred to is a fine imported dry cider.
I never said anything about whether sweet or dry was better, just that the earlier the ferm was stopped, the sweeter it was. I personally like dry cider as well, but with some apple taste. I will stand my ground that, especially with store bought apple juice/cider, those last few points seem to be the difference between a nice dry apple cider, and cheap flavorless white wine. This is from my limited experience with ~7 batches, but there is more than enough corroborating evidence in the cider forum.
The yeast eat, or somehow get rid of, flavor compounds as well as sugar. I have heard some is metabolized, and others get fixed to the yeast as they flocculate and settle out. Whatever the cause, it seems that when sugar starts to run low, the apple flavor disappears. This is true for many flavors added prior to ferment.
If you have the luxury of access to true high acid heirloom cider apples, maybe going to completion would still leave some apple taste. With store bought stuff, it doesn't. It is tricky to catch it just right for a dry cider, but still retain some apple taste. Many of the fancy dry cider makers, if not most of them, ferment to completion, and then add back in some fresh cider or concentrate to give it some apple taste. This "backsweetening" is also popular with homebrewers to avoid having to monitor the ferm, but still have some apple flavor and, if desired, sweetness. These methods, along with their pros and cons, are discussed thoroughly in both of the threads I referenced.
As for Woodchuck and the like, all I taste is Jolly Rancher and sugar. I suspect there is some "apple flavor" as well as plain sugar backsweetening going on.