Well, first of all, I don't believe constant-speed props or piston engines, used in today's aircraft are complex systems - perhaps they were 50-60 years ago, when they were developed, but not in 2011. Besides, I believe electric engine efficiency, just as in piston engines, is achieved if they are run at constant speed - so you need some kind of speed control in both cases.
The weight saving really made me smile
According to
Shell, the typical energy density of 100LL fuel is 44 MJ/kg, while the current Lithium-ion batteries in production don't reach even 1 MJ/kg. So basically, for the same weight of fuel, you get 44 times more energy with using 100LL. And on the plus side, when you burn the fuel, the weight of the aircraft decreases, so you need less power for same speed, reducing the fuel flow and thus increasing efficiency. With electric power, you still need to carry batteries around (unless you get rid of them in-flight, but this wouldn't be neither pro-environment neither economic).
I know the weight saving in small aircraft aren't large. But think for example of a transport aircraft, which flies on a transatlantic route. If we assume the fuel usage is ~ 150.000 liters of Jet A-1 (I googled the data, but I think it's a good estimate), this turns out to 123 tons of fuel, which (if using energy density of 42,8 MJ/kg) turns out to approximate 5.260.000 MJ of energy, which you need for the flight. Again, if we say that current batteries have energy density of around 1 MJ/kg, that means 5.260.000 kg or 5260 tones. Seems to be rather exponential increase of weight, not decrease if my math is correct?
Another problem is the energy flow problem during charging/filling up the aircraft, which is basically the same as we see with hybrid/electric cars. While I don't have the numbers for fuel flow for gas trucks on airports or electric system of airports, I can provide you with a comparison based on home electric system and car fuel stations. Let's say we use 230V system with 20A fuses. If we run this to the limit, we get 4,6 kW electric power, which indeed means 4600 J/s or 16,6 MJ/h. Our local fuel pump has a diesel fuel flow of around 0,5 l/s (probably a little higher, but let's stay conservative). Fuel flow of 0,5 l/s means that we pump 1800 liters in an hour, which (with diesel fuel's energy density of 35,8 MJ/l), this turns out to 64.440 MJ/h, which basically means more than 3800 times higher energy flow than with typical home-based electrical charging.
PS: I am no expert on subject of electricity, but I think this rough numbers are quite accurate for objective comparison.