My guess would be electric might be simpler and easier to maintain and with electric you can charge at home.

mass per kilowatt hour. That is the magic number. While a gas turbine can be slightly over 52% efficient it weighs a lot. You can plot weight over kilowatt hours, which is useful since at small numbers of kilowatt hours batteries are a huge win, and then at some point you get a cross over where the fact that fuel is more energy dense it has compensated for the weight of the turbine and generator infrastructure.

Not my area of expertise here, but since quadcopters are all about torque, I speculate that electric motors (with their flat-ish torque curve) are much easier to design for?

I've thought the same thing, perhaps efficiencies for generating electricity for fuel engines are too low currently? Anyone have any stats?

Maintaining EVs is cheaper and easier than fuel-based vehicles.