The web site UtahFishFinder claims a 99% survival rate (assuming the fish hit the water). I presume height of drop could influence it. They drop the fish anywhere between 50 and 150 feet:
Once he's over the desired lake, the pilot evaluates his approach and exit, plane speed, windage and altitude, and lines up with the lake. While over the lake, he triggers one or more of the toggle switches on the plane's instrument panel. This opens the compartments, allowing the water and fish to drop into the lake below. The fish fall between 50 to 150 feet, depending on how close to the lake the pilot can fly.
Because of their small size, this process of dropping doesn't hurt the fish (it's like a high diver diving into a deep pool of water). The survival rate of these fish is around 99 percent.
At Glenn Air Alaska they fly higher, up to 250 feet. The survival rate is nearly the same, at 98 percent:
Years ago, Glenn and Martinek had the hatchery crew videotape the aerial operation and learned that dropping the fish from 250 feet produced a 98 percent survival rate.
"Two-hundred-and-fifty feet is just right," Glenn said. "The water atomizes. The fish are in the air just long enough to orient themselves so that they hit the water head first and not long enough that the freefall dries out their gills."
In contrast, the Western Canadian Game Warden, do not specify a drop height. The success rate in their studies is over 85 percent:
The Colorado Division of Wildlife (DOW) stocks native cutthroat trout in high altitude lakes with airplanes. Four specialized pilots fly modified Cessna 185 airplanes and stock around 300 lakes ranging in altitude from 10,000 to 12,000 feet. Several hundreds or even thousands of fish are dropped at a time. The airplane is equipped with a custom built trout tank, named “Bass-O-Matic”. DOW studies show that over 85 percent of the tiny fish actually survive the fall.
The Airplane Owners and Pilots Association published a piece on Maine Game Wardens, indicating
Department biologists using scuba gear have had trout dropped around them and observed as the fish hit the water and swam away. The biologists report that most of the trout easily survive their aerial drop without injury or harm.
(I'm not sure I'd volunteer to be under a fish drop, but it would be an experience.)
Compared with loading the fish up on mules, like in the old days, the shorter plane hop to high alpine lakes likely means fewer fish die on the way, more than making up for any losses during the drop.
Edit - the BBC has just posted a video of a drop by the Utah Division of Wildlife Resources. They state that 95% of the fish survive the journey.