For weekending and other short hikes that do not require resupply, I use Esbit. I had an unfortunate experience with alcohol last year and prefer to avoid it on safety grounds. I got soaked with alcohol and torched myself while wearing a nylon shirt. Scary and painful. This was after using alcohol since 1973.
Furthermore, Esbit is the most weight-efficient fuel for any unsupported trip length.
Things change when local resupply is an issue. For the AT in '07, resupplying locally (I don't do mail drops unless absolutely necessary)I plan to use alcohol for its convenience. I recently put together a dual fuel system so I can use Esbit when it is available. Burner and pot support together weigh 0.25 oz. Not too shabby.
Why use a dual fuel system on the AT? Sometimes one fuel is easier to find than the other. I have been in towns where denatured or Everclear is 5 miles down the road, but the hardware store has a Coghlan's rack or a stack of Esbit. And sometimes the only thing available is yellow HEET and Esbit is unheard of. Versatility means not having to carry too much extra fuel.
My duel fuel system is a fiberglass insulation-filled tequilla bottle cap. Turned upside down, it's a platform for the Esbit. This works fine with tea light cups as well. I was worried that Esbit might burn through them as it burns oven-liner weight aluminum wind screens. However, they don't seem to heat up much at all.
The revelation that led to using the "tea light" stove was that I discovered accidentally that it was just as efficient as any other alcohol stove I have made (scores of them) The heat output and burn time are directly related to the diameter of the cup, and the burner should be matched to the pot diameter for greatest efficiency.