I've tried clear apple juice and unfiltered apple juice or cider. The only difference I have noticed is that there is much more sediment with the unfiltered/cider than there is with the clear apple juice. All three tend to clear out very well if/when given enough time.
As far as taste goes, both were very good, especially when given time to age a bit. I googled the difference between the two (apple juice and cider from the store), and it looks like the only major difference is the filtration.
Based on this, I'd say that yeast and aging make more difference than anything, as long as you start with an "acceptable" apple product that is 100% juice (or natural cider) that is free from preservatives and so forth as discussed above. Of course, different brands are made up of different blends, and that will also affect the final taste. It seems to me that it is mainly a factor of finding the combination of apples, yeast and aging that you like. From there, of course, you can experiment with carbing or not, as you prefer.
I would not call this a very scientific conclusion, but rather an observation that has led me to conclude that there are bigger things to worry about.