[chris (OP)]

How do white and brown sugars differ; is brown sugar "healthier" for you?

[chiralSPO]

I doubt there is any significant difference in "healthiness." Both are essentially sucrose. Brown sugar usually also has some monosaccharides (glucose and fructose) and some very minor impurities that add some color and more complex flavor (as well as traces of vitamins and minerals, but not likely to be dietarily useful at healthy doses of sugar). White sugar is just a little bit purer, and is also often bleached (making the impurities less dark, not necessarily less of them).

[Hayseed]

A very long time ago, I worked in a sugar plant, which processed beats.

The beets are juiced, filtered and the brown juice is cooked into a syrup, called molasses.  I understand cane has a similar process.

There were microscopes inserted in the vacuum heated vessels, and at a certain specific gravity, if I recall, the sugar would start to form crystals.  At the right time and crystal accumulation, the molasses is dumped into a series of centrifuges. 

One can spin out any shade you want. Brown sugar is still slightly coated with molasses.....juice.

Brown sugar has sugar juice.  More nutrients and less calories.

[Bored chemist]

Brown sugar has sugar juice.  More nutrients and less calories.

How many fewer calories?

Essentially the difference is that brown sugar has a little more caramel and a lot more marketing hype.

[Hayseed]

The calories will be proportional to the number of sugar crystals that are replaced with the nutrients, in the weighted product.  And over here, it's probably regulated now.

[Bored chemist]

It's interesting to see caramel and junk  described as "nutrients"

[chiralSPO]

Some of the "junk" is nutritious.

During the sugar refining process they start with a liquor which is essentially ground up plant matter that is rich in simple sugars. As the sugar are selectively crystallized out, the remaining liquor becomes concentrated in everything other than sugar, which includes potassium, magnesium, iron, manganese, and other minerals, as well as some vitamins (depending on what processes are used--these vitamins might be destroyed or not)

I don't know how accurate these data are, but at a glance, they are in line with what I would expect to find in molasses: http://whfoods.com/genpage.php?pfriendly=1&tname=znutrientprofile&dbid=85

[Hayseed]

We sold the excess molasses as cow-feed supplement.

[Bored chemist]

We sold the excess molasses as cow-feed supplement.

Molasses is still mainly sugar.

[Hayseed]

I can't recall what the spin waste was called.  But many venders bought it.

[Hayseed]

I had to look it up.  The liquid that is poured into the spinners is called liquor. It's raw molasses.

The spinner separates the crystals from the liquor and what's left is commercial molasses.