I think it's actually around 30 miles between the two stadiums. Could argue that it's only 20 miles being some of the fans local to each stadium though.
On that note, it wasn't long ago that Emirates wanted to repaint the Spinnaker tower red... it caused uproar simply because it was Southamptons colour. People still moan that they made the logo red on the Spinnaker tower website.
My girlfriend is from Portsmouth, and she used be a ST holder there. The word 'Southampton' is like a swear word to a lot of people in Portsmouth. They haven't played each other for a while because of Portsmouth's drop through the divisions, but the hatred still lingers.