Just to clarify, the electric Bic does not use a battery. The piezo ignitor strikes a quartz crystal when you push the button, which creates an electric current. The ignitor will eventually wear out, but you'll probably deplete the fuel long beforehand. I've never had a Bic piezo ignitor fail, and I've used up a number of lighters.
That said, it is not necessarily true that the piezo Bic holds more fuel than the flint model. The added bulk and weight may be entirely due to the piezo ignitor.
We could test to see: buy one of each model and weigh both. Tape the button down to jettison the fuel. (Blow the flame out so it doesn't melt, and do this outside!) Then, subtract the empty weight from the full weight to determine fuel capacity.
This might be splitting grams, but consider that the flint is slowly consumed with the traditional model, further reducing its weight.
For low-altitude trips, I'm ambivalent about which to take. For the PCT thru that I'm planning, I'll avoid piezo ignition due to its unreliability above several thousand feet. In my experience, a wet flint Bic will work again once it's dry.