The difference is so slight as to be negligible. While honey does contain some antioxidants, there are lower calorie sources of those. Basically, honey is just another form of sugar with a slightly different flavor.
What Manda said. Unless you plan to eat several cups of each per day, it's sorta a wash.
Honey is (usually) less processed than sugar (even natural, organic sugars), and it does contain antioxidants. It's also easier to buy honey locally and support local farmers, businesses, and so forth. So it would be a better environmental choice from that perspective.
OTOH, if you're Vegan, there are issues with the use of honey - from the involuntary nature of the harvesting, to the fact that bees do die in the process. In that case a natural cane sugar would be a better option.
The only real advantage I can think of is the lower environmental impact than sugar, due to all the processing that sugar goes through, and the fact that sugar may have to travel farther to get to you (it's easier to find local honey).
Other than the fact that it tastes so good with peanut butter. Yum.
I also heard that if you have problems with outdoor allergies, that you should seek out local honey, and eat a small amount every day. It is supposed to help with the allergies, because the honey will contain compounds from all of the local plant life in your area...
I don't know if this is actually true, but I have read that honey is "sweeter" than honey...while calorie-wise they may look the same by the teaspoon, it takes less honey to attain the same level of sweetness as the sugar so you don't have to use as much. I think this may bear out to some extent because I have noted that often in a recipe, if it says you can substitute honey for sugar, less honey is called for.
Hmmm...I should have said ABOUT the same calorie-wise by the teaspoon...but I'm thinking those 6 extra calories in my tea were not what made my rear end grow beyond my comfort zone.