A lot of people use honey because a lot of people recommend it.
Honey does have the hypothetical benefit of possessing various trace vitamins and minerals, but it's unclear if these actually provide any sort of tangible benefit. Some add a tiny dash of sea salt to their sugar water to achieve a similar injection of minerals/electrolytes. It seems reasonable to suggest either of these would do more good than harm, but a healthy colony should be capable of getting all this from their protein sources.
As Kevin said, studies done on quite a few species of ants show a clear majority prefer sucrose. That said, it's worth noting the enzyme(s) which breaks down sucrose in ants produces fructose and glucose. Honey is primarily composed by two types of sugars, drum roll please, fructose and glucose. There's a bit more fructose than glucose, but the ratio is close enough to 1:1.
While there are plenty of studies showing ant preference, I've never heard of anything suggesting a colony does better when fed exclusively on one or the other. If you use honey, just make sure your poor little workers don't get stuck and die. They're like toddlers looking for a fork and an outlet sometimes.
For the ant species people are likely to keep, just make sure they have SOMETHING available and don't stress about it. Sugar water (sucrose) is cheap, though, and it stores very well in a squirt bottle. Honey water... doesn't. I like to give my founding queens a honey snack, but my colonies get nearly constant access to sugar water.
Edit: I know some people here have strong opinions on AntsCanada, but he provides constant sugar water with a weekly treat of unpasteurized honey. That might be a good compromise for you, if you can't make up your mind. Oh, and obligatory "honey could be tainted with something bad", though, unlike with pesticides on fruit, I've never heard of it happening.
Edited by Antsinmycloset, April 19 2017 - 9:27 PM.