Use of Heaviside operator versus Laplace transform in electrical engineering
The operator method introduced by Heaviside was empirical. It did work, but no formal proof was given.

The Laplace transform has a mathematical foundation and can even be used to show the correctness of the operator method. 

The Heaviside method is not as general as the Laplace transform, for example it is not possible to have initial conditions.

So the Laplace transform is the more modern and more advanced method and is therefore preferred.