One thing to note is that hybrids have the potential to seamlessly do one hypermiling trick, at the cost of abusing the batteries badly.
One popular trick for hypermiling, especially on gasoline engines, is "pulse and glide" - get the throttle open pretty wide, reducing pumping losses, accelerate, then shut down the engine and coast. Repeat indefinitely.
A hybrid can actually do this without changing vehicle speed - shut down the engine and run electric only, then once the battery is depleted, restart the engine, and switch to regenerating from the electric motor(s) while the gasoline motor is propelling the car.
Works better on a flywheel or hydraulic hybrid, though, rather than a battery hybrid.