Omar is correct, but:
The Mirror Modifier definitely wins.
The Edit Mode Mirror is quite 'buggy' and even if it wouldn't have been buggy, it still wouldn't mirror things, but it would just Transform Vertices that are 'mirrored' in a mirrored fashion. I hope that makes at least a little bit of sense.
Edit/Sculpt mode mirror doesn't mirror geometry. If the geometry is close, it can help to manipulate it, but as mentioned above, if it's not perfectly symmetrical, things might not work like you expect, especially if it gets turned on when the mesh is not perfectly symmetrical to begin with. Mirror Modifier is an exact mirror... what happens on one side WILL happen on the other side, whether it be adding or manipulating geometry.
Both can be useful, as long as you know what to expect.