I believe electric bicycles produce less carbon than regular bicycles because it takes a lot of carbon to grow and create the food we eat to power our regular bicycles.
I'm pretty sure this holds true if the regular-bicycle rider eats like the average citizen of a first-world country. But probably not, if we're talking about somebody who mostly eats locally grown non-industrial-agriculture type vegan food.
In any case, 40 to 200 pound e-bikes are so much more efficient than 3000 pound economy cars, there's almost no comparing them.