The main benefits of using a magnetic stirrer over a mechanical stirrer is that it is much quieter and apart form the stir bar, nothing comes into contact with the flask or liquid prolonging the life of the unit. The stir rods can be sterilised easily but may break down over time as their construction (a metal magnet inside a plastic coating) is fairly simple. Stir rods can be purchased fairly cheaply from lab suppliers. The magnet is covered in the plastic or a glass covering to make it chemically inert, allowing it to be submerged in liquids without affecting them.
Some magnetic stirrers have a heating function which can heat the flask from below, some have a variable speed function. In very viscous liquids, the stir bar may only be effective rotating at the slower speeds whereas when making a solution from heavy crystals (CuSO4 for example) a fast speed usually helps dissolve the solid quicker.