You still need a battery bank to store the electricity. You still need to charge the batteries. You still have every other part of the electric car
So, then you are realy asking, first, is it more efficient to:
use the electricity from the battery to turn an electric motor
battery--> electromagnetic effect (motor) --> turns which turns axle ( wheels)
or, use the electricity from the battery to make heat to turn a stirling engine motor
battery -->electric heat element --> stirling engine (motor) --> turns which turns axle ( wheels)
generally speaking, each time you convert energy from one form to another, you have conversion losses, and a regular electric motor, electromagnetic effect, is very efficient. Losses are due to the physical act of turning, friction, which the external heat driven engine ( stirling engine) also has.
the second thing you are asking would be difference in materials, so rare or environmental differences. Again, both would use the batteries, which are the main problem component.
What is in an electric motor ? Copper windings ? What is the parts that you are concerned about ? Electric motors usually have no permanent magnet, as current thru coils can be used instead, or they might have a few permanent magnets. Thare are many ways to make an electric motor, I think you do not need to have rare materials magnets, although they may be used for space/weight or other considerations.
https://en.wikipedia.org/wiki/Electric_motor
a third, potential issue to compare the 2 motors, electro-magnetc or stirling effect, would have to do with suitability to drive the load. I dont know if a stirling engine is suited or not, but that would be a consideration.