An airport with SOU's accessibility and BOH's runway and land area would trump any other airport on the south coast and would no doubt have the potential to attract considerably more business than both BOU and SOU combined. However that's not the case and each trades off the other weakness, meaning there is room for two 'compromised' south coast airports rather than a single 'perfect' airport. I don't see anything changing in this respect.
SOU - compromised by its runway and apron, suits the short haul business markets
BOU - compromised by its accessibility, suits medium haul (and potentially long haul) LoCo and Charter leisure markets, plus aviation services such as Cobham.
I am sure both have scope to expand and prosper based on their respective areas of strength as the demand and the economy allow.