dogman said:
I don't know that answer. Usually the lower voltage motor will be slower, and then go further due to less wind resistance. The more typical thing would be to have controllers of similar amps, and the voltage is the variable. I would guess, though, that if WOT on both the 24v 20 amp and the 48v 10 amp were producing the same speed, they would both be equally efficient at WOT. What happened between start and full speed might be better with one of em but I can't even guess which it would be.
Just going to elaborate here.
Watts are watts. Unless the motor has different efficiencies at different voltages, then it really doesn't matter how you put the watts in. Having said that, I played with the ebikes.ca simulator and there does seem to be slight differences in overall efficiency at different voltages, with lower voltages being slightly more efficient. I'd guess it's due to internal resistance in the batteries. Playing with the simulator is the number one way to get a feel for performance without spending money. That simulator is a fantastic traffic pull to the ebikes.ca website.
The main reason people usually say that volts=speed and amphours=range is very basic. If you have the speed, you're more likely to use it. Unless you are deliberately choking your throttle, then you're going to see more range at lower voltages and higher capacities. If you're riding deliberately for range, then there will be very little difference. It's also much easier to pedal along at lower speeds unless you have that godugly but awesome 58 tooth chainwheel that Dogman has.
The single most important thing for range is wind resistance. It's a cubic. So going twice as fast burns 8 times as much energy to cut through the wind. The effective range differential between 15mph, 20mph and 25mph is huge.
Then there's hills. The most efficient way to climb a hill is at a speed where wind resistance drops off to negligible values compared to the work required to gain gravitational potential energy (less than 15mph), but not so slow that your motor stalls. So look for a throttle value that gives you good efficiency and output energy at less than 15mph and stick to it.
Play around with the simulators and you'll get a good feel for it.
http://www.me.psu.edu/lamancusa/ProdDiss/Bicycle/bikecalc1.htm
http://www.ebikes.ca/simulator/