On a flat Earth, north would be the dead center of the Earth. South would be the farthest point away from the north pole in any direction so long as it is a straight (STRAIGHT) line. Basically, a line segment drawn from the very center of the Earth (which would represent the North Pole on the Round Earth) to the outer edge of the ice wall's (where the Earth stops and the great beyond begins) two points (starting and ending) would give you the exact positions of the North and South poles on a flat Earth.
Now.
Any time you move perpendicular to the North pole (facing it), you move either West or East depending on which direction you move. If you were to move West forever (non-stop) you would be going in circles. If you were to suddenly stop, the center of the Earth would always be North (since it is a point) and South, if you were facing the North, would always be directly behind you.
Basically, you can go West and East for all eternity. North stops at a certain location (on a round Earth, once you hit the exact north pole, going north from that location would be going south) and South stops at the end of the Earth. It is impossible to go North and South forever on a round Earth as it is impossible to go North and South forever on a flat Earth. The difference, however, is that you cannot continue going south after reaching that farthest point on the ice wall and proceed to be going North. You would presumably fall off the planet.
To sum it up:
You can go East until you hit the exact same location on a Round Earth and a Flat Earth.
You can go West until you hit the exact same location on a Round Earth and a Flat Earth.
You cannot go North until you hit the exact same location on either model. As you pass the North pole, you will begin to go South and by that fact you will no longer be going the same direction.
You cannot go South until you hit the exact same location on either model. On a round Earth, as you pass the South pole you will begin to go North and by that fact you will no longer be going the same direction. On a flat Earth, direction stops at the South pole because that is the end of the planet. There is no direction at that point except moving away from the flat Earth.
Therefore: I can safely say I can go only one direction and hit the same spot on a Round Earth as on a Flat Earth so long as it is not North and South, which would be impossible to do on either model.