At least in the sport flying realm, electric power is rapidly overtaking glow fuel power in all realms of model aircraft - radio control, control line, free flight, as well as in helicopters. Beginning in the mid-1990s, there have been an increasing number of competition classes that specify electric power as well.
There are many advantages of electric power - much lower noise, consistent power, higher power-to-weight ratios (using brushless motors and Li-Po batteries), no need to use fuel-proof finishes, no oily residue, much lower vibration (allowing lighter airframes), less Volume required for most motor/battery/controller systems than equivalent engine/fuel tank/servo system. Of course, some people love the noise and mess from the traditional internal combustion engines and wouldn't give them up for anything.
Disadvantages include somewhat higher entry costs for electric, multiple batteries needed for aircraft to avoid long downtime between flights, low noise level can make it difficult to tell if motor is running at long distances (of course, if the airplane goes down with the throttle up, that's a good sign that power has been lost).
I am going to collect some videos showing how successfully electric power has been.