You do not require an electrician to replace a breaker box of an electrical panel if it is not the main pain to the house. A permit is required to replace a sub-panel as well as the main electrical panel. Although a homeowner can pull a permit to perform a sub-panel replacement it is highly advised that you contact an electrical company to perform the task.
To replace a breaker box will vary in cost depending on if you are replacing a main electrical panel or if you are replacing a subpanel. Subpanel replacements cost less due to the number of circuits involved as well as the fact you don’t have to disconnect power to the service because they have a separate disconnect for just the panel.
A breaker box uses circuit breakers that both provide thermal and magnetic circuit protection, a fuse box will have fuses to limit the current by means of thermal protection.
A breaker box is dangerous just as all electrical devices are considered dangerous. Electricity is dangerous, plain and simple. A breaker box is no more dangerous than your plugs and switches in your house. It should be handled with respect and extreme caution. Only qualified individuals should touch any electrical throughout your home.