Lighter planes are more efficient, and most airliners are not designed to land with their tanks full. They have a option to jettison their fuel in case of emergency.
It means that just matching the energy density of fuel is not enough, batteries must exceed it. Jet engines are also quite efficient: around 40% now, and it may reach up to 60% in the future. It means that the more efficient electric engine is less of an advantage compared to cars for example.
The only battery technology that seems viable in order to replace fuel would be lithium-air. Petrol is just too good at storing energy.
Right now, I'd say the only chance for a "zero-emission" plane would be using biofuels.