I've tried carbonating with honey since I'm a beekeeper and tend to have it, but sugar really is cheaper, much easier, and gives the same results. The tsp or so of honey you need to carbonate really doesn't add enough flavor to warrant the mess. I played with a cyser to make the honey stand out. Huh. That's been cellared a while, too. Time for a taste test, methinks!
We are very lucky -- we've got a nursery in the area that grafts cider-based variants, not just the eating apples. The varieties we went with are Honeycrisp (for eating and for sweetening), Bramley's, Northern Spy, Dabinett, and Michelin. They're on a variety of dwarf and semi-dwarf grafts. This is the third or fourth year, so I'm not expecting a great crop until next year. Last year we were able to press a couple of gallons, so we just went with what the trees gave us. Next time I start quantifying the cider contributions for real.
The place we bought came with an old, neglected apple orchard, so we've made cider from these mystery apples with very good success. Some probably more an eatin' apple, since they're on the sweet side, but other trees tend to have more of a bitter mouthfeel. So far, I find that if the pressed cider is drinkable as-is, but leaning toward dry/bitter, the cider is more what I want.