It depends on how frequently you want to communicate with your end-users when a service is unavailable. If it is just a matter of communicating with them in advance, a broadcast may be sufficient. Also, if linking incidents is important, broadcasts is the way to go. Broadcasts are displayed in the header in Self Service and Console, attracting the attention of the users.
Service Health must be invoked from Self Service. It allows the service management team to issue regular communications throughout the duration of an outage. For unplanned outages, this is important to set expectations with end-users. For planned outages also this may be important if the outage is expected to exceed the planned duration of the outage.
Depending on the merits of each solution you may decide what's best for your organization.