Have a look at http://www.thru-hiker.com/articles.asp?subcat=2 for a couple articles comparing cooking system weight over time between various choices.
In those examples, the white gas stove specified weighs enough to offset the weight savings due to fuel. That might vary depending on stove model chosen.
A factor to also consider is fuel availability; both gas and alcohol are available on the AT every few days, so you normally wouldn’t need to carry more than a week’s worth of fuel at any given time. (Obviously this will vary depending on hiking style and probably some other stuff as well)
Another thing to remember is that with alcohol an fluid ounce doesn’t weigh an ounce. If I remember correctly, alcohol weighs about 80% of water, and thus a fluid ounce weighs approximately 0.8 ounces. A 20oz soda bottle filled with alcohol should weigh 16oz plus the bottle weight.
On my workbench I can reliably achieve a rolling boil of a pint of water with 13gm of alcohol fuel, which is roughly half an ounce weight-wise. Add some fudge factor and figure in trail use I can get 27 pints boiled per pound of fuel. At three pints boiled per day that’s still 9 days of cooking. Assuming white gas is twice as efficient, you’d use half a pound of fuel in that time, so your fuel weight savings with gas is half a pound over 9 days. To achieve a net weight savings, a white gas stove must weigh less than half a pound more than the alchol stove, making sure to add in pot supports, windsceens, etc.
On the other hand, if you were going out for a month between refueling stops and boiling three pints a day, the fuel weight savings add up and would eventually make white gas the more efficient.
This is all assuming fairly moderate temperatures; in cold weather you’ll of course use more fuel. With temps in the mid/low teens and below then you’d probably want to choose white gas even if it has a weight disadvantage due to white gas working a bit better in the extreme cold.
deeddawg