What is an advantage of using an electromagnet rather than a regular magnet?

Controling: It is a magnet when you want!

Suppouse you have a permanent magnet, i.e. regular magnet with your words. Then you have is constant. You can not change it. Or turn it off when you do not use it.

But the case is totally different for electromagnets. By sweeping current passing through the circuit you can tune the magnetic force you will. Only restriction is on cables: They can carry only a limited amount of current. But if you choose proper cables for your job then you will not have any problem.

If we denote maximum field associated with the maximum current with ##B_{max}##, then you can tune any magnetic field value in this range, i.e. you have a continious range of magnetic field:

##0\leq B\leq B_max##