The default position for most people living on the south coast in Hampshire or Dorset, is to use the airport that offers the route, schedule and fare that works for their needs. That invariably means , LHR, LGW or LCY, with the added bonus of a chance of a flight from either SOU or BOH if the Schedules work (nine times in ten they don't) even though the coastal airports are usually the preferred 1st choice.
BRS and EXT are usually just too hard to get to in a reasonable time and almost never feature in plans.
It's almost never a toss up between SOU or BOH, just not enough flights from either.