I believe most commonly used batteries on modern electric subs are Li-ion cells (pretty much like the rechargable batteries in most power-tools and consumer electronics). Low maintenance, no environment impact (which is a huge issue since a sub is a closed environment) and high energy density.
Nowadays, electric subs are always constructed so that an electric motor, powered from either batteries or the generator, drives the propellers and you have some primary propulsion (diesel, AIP etc) driving the generator behind it. Main reason for this is that you really don’t want your noisy diesel engine connected to the propeller-shaft as that would transmit a lot of unnecessary noise into the water.
Its too bad there isn’t a device that can generate electricity directly from radioactive material without any moving parts.