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[Phys-L] batteries vs capacitors



Hi.
I am wondering about the tradeoffs associated with using a capacitor vs a rechargeable battery.
I am working on plans for an E&M project for my students. It is a high school physics for everyone class. We have covered basic series & parallel circuits, magnetism, em induction and so on. The induction part and all e&m right hand rule stuff has been qualitative (for this phys for all class).
I am going to let them make their choice of:
a 1 string electric guitar,
a speaker,
a shaker flashlight.
Each of this includes a bit of circuit content and some magnetism etc...
I am at my limits when it comes to storing charge in the shaker flashlight. I have made quick shaker lights where the led lights up during the magnet moving back and forth through the coil. I haven't made one that stores the energy from the induction that will be used with the flip of a switch.
I believe I have things figured out in terms of the circuit diagram, diodes, switch location etc...
I am not sure of the tradeoffs associated with storing the energy in a rechargeable battery vs a capacitor.

Any insight?

Thanks for the help.
Paul.