If the plane is nose heavy it will fly with no noticeable difference. What you will notice is that in turns or inverted the nose will drop. You will also notice that the plane requires more elevator to bring the nose up in straight and level flight or during landings.

If it is tail heavy, you will require no "down elevator" to keep it level or may require up elevator. The second thing you will notice is that on landings or slow speed approaches, the tail will drop.

For many aerobatic maneuvers, a slight tail heavy condition is desirable.