Saint Sheldon had this to say:
Originally Posted by Sheldon Brown
Most hubs in current production are "small-flange" or "low-flange" designs, where the flange is no taller than it needs to be to provide a suitable place for the spoke holes to be drilled.
"High-flange" or "large-flange" hubs have a larger flange, usually drilled out for lightness. They transmit torsional forces with less stress to the spokes than small-flange hubs do, but this is not a problem in practice with modern equipment. High-flange hubs can make a wheel with slightly greater lateral strength than equivalent small-flange hubs, because the spokes create a wider bracing angle to the rim. This makes them popular with track sprinters, who create greater-than-normal side loads on their wheels.
I have a couple of bikes with high flange hubs, and several with low flange hubs. Frankly, I can't tell the difference doing the type of riding I do, which is mostly casual. Maybe if I were a pro rider putting out a lot of power I'd feel the difference.