is a higher voltage battery a more efficient energy deliverer than a lower voltage battery?
Any given motor will develop torque proportional to current.  However, within some reasonable power range motors can be built with considerable latitude in their voltage versus current tradeoff.  For example, a 1 kW motor could be made for 100 V 10 A operation, or 200 V 5 A operation.  Once the motor has been chosen though, you're stuck with that tradeoff.

This tradeoff doesn't go infinitely in both directions due to practical limitations.  If you use too low of a voltage, then the current becomes so high that conductors need to be thick and expensive.  Note the losses is wires goes with the square of the current, or put another way, for the same power loss you need copper proportional to the square of the current with DC.  With AC skin effect gets in the way and makes things more complicated.

At the other end, high voltages become difficult to handle and keep safe.  Above a few 100 Volts, electronic components get a lot more expensive and you have significant safety issues.