When solving a question using Energy or Net Force methods, should I be getting the same distance?

Yes, your answers should be the same. The approach you use doesn't change what actually happens. Chances are you're making a mistake somewhere in your calculations. Remember that when calculating the work done on the cart by the force of gravity, you only use the component of displacement along the direction of the force. (If the cart is going up on an angle, you only can consider its vertical motion.) Using conservation of energy, you can pretty easily find that h = v^2 / 2g, where v is the initial speed. (This is assuming no friction force, which doesn't complicate things too much really.)

Should be the same answer.  Assume the total energy of the car is TE = PE = mgH which is all potential energy as the car sits H height above the ground level.  By conservation of energy, assuming no friction losses, we have PE = mgH = 1/2 mV^2 = KE the kinetic energy after the car drops H to h = 0 at ground level.  Now it starts back up.

The force F = mg = W is the force of gravity that reduces the KE to zero when the car again reaches H.  We call that force of gravity weight.  So the work done to slow the car down is WE = Fh = mgh = mgH = PE = TE where the total energy is back to only potential energy because V = 0 at the top of the loop.

And there you are.  The force F = mg = W the weight of the car.  And the work is just the force times distance work function WE = Fh = Wh = mgh = mgH to raise the car weighing mg back up to a height H against the force of gravity.  My point, you need to know the force to work the energy.