This is usually a family decision. A lot of the debate ends up being dictated by how much room one has available. You can typically fit the same electronics into either space. If the space is not the issue, The decision usually rests on a few things. Sound and light are usually easier to control in a dedicated room environment. This means quality of sound in the room as well as sound leaving the room and sound invading from the kitchen (arguably the loudest room in the house which seems to always share the family room).

Dedicated rooms are good at Impressing the neighbors and friends a very popular reason that most won’t admit too (not at first anyways).

Family environments are nice because they are less formal. Typically any house we install a dedicated media room we have surround sound in the Family room as well. You get used to  hearing clear dialog at any volume level rather quickly.