In my picture posted above, it's easy to see the relative specific energy (energy density or power density) of various sources of power. What's less simple to understand is the relationship of powerplant efficiency to real world output.
Put another way, a gasoline engine at 33% efficiency will consume 3 times more energy than a battery/motor combination at 100% efficiency (silly example, I know)
So, while the differences are not as great as the chart shows, battery powered aircraft will remain quite limited.
Electrochemical energy and it's physical - theoretical limits are well known and understood. For practical, real world parity, electrochemical energy would have to improve beyond the limits of physics.
Consider powering an airliner by batteries, for example. The level of energy required is massive. And, no matter how fast you could drive the fan with an electric motor, you still don' have the heat, pressure and thrust of the core engine (all key factors in high speed flight) .