Simple sugars are all processed the same by the yeast- they don't differentiate between corn sugar and beet sugar, for example.
The differences in flavor may be perceptible to you, however, as brown sugar is white sugar with molasses added. Once the sugar is fermented out, there may be a slight "molasses" flavor left behind. The level of "hotness" generally is only attributed either to the ABV or the fermentation temperature, although if your experience is different I can't explain that.
Honey has very little nutritive value to the yeast, so it's a slower, harder ferment for the yeast. It can stress the yeast in large amounts, and yeast nutrient is commonly added.