I've made Apfelwein every which way til Sunday...
The original recipe, with Dextrose (corn sugar) will ferment out completely, leaving a subtly tart and sweet product. This also clears the fastest, due to the complete fermentability of the Dextrose.
Cane sugar (table sugar) will ferment out very well also, but will leave the finished product slightly sweeter, and will take slightly longer to clear.
Dark brown sugar will ferment out quite dry, and will finish with a darker, more tart product due to the extra molasses. This takes about twice as long to clear as the Dextrose.
Honey depends on how much and when you add it, if you add 3 pounds at the beginning, it will ferment out very well, with a somewhat dry finished product. If you step it (add a little at a time), then there is a chance you can bump the ABV up quite a bit, and leave it very sweet. Honey takes the longest of them all to ferment and clear, your looking at at least a few months for this.
That said, I assumed from the original post (using organic cider, not apple juice) that you are making a New England (or Common) Hard Cider, not Apfelwein. Hence my original vote, and first post stating nothing but cider and yeast, with a little corn sugar if you're just looking to bump up the ABV a little. My New England Hard Cider generally comes out about 5 or 6% with no sugar added.
Whichever route you decide, let us know how it comes out...