Spin uses the Z axis of the object as the pivot point and the first and last points should be at the same X coordinates otherwise the object will be lop-sided. Sweep, on the other hand uses the first and last points of the outline as the pivot.
Z . ------- FRONT VIEW . / . / . / . / . / X................./... . / . / . / . | . | . |_____ . | .--------- .
If You Spin this object the top will be closed with its centre offset. If You Sweep it the top will be open and symmetrical.
You have to remember:
Spin is useful when trying to build a closed top/bottom lathe object (paying care that the first and the last points of the outline fall right on the Z axis), since Sweep fails in this. Also Sweep is to be used when the outline to be spun is a closed one (e.g. when making a torus of a circular outline) since Spin is definitively not recommended for this.
SP & SW always rotate the object along the local Z axis of the object, so You can obtain different kind of rotations by moving or rotating the object's axes only (select "Transform Axes Only" in the Transformation Requester or press the Shift button in interactive mode).