Loyalty to Brighton runs through the generations, in towns and villages across most of Sussex (though I would say not in Crawley). The Amex has drawn many lapsed fans back and re-energised dormant ones.
I really don't think Crawley Town have this kind of catchment. There are about 100,000 people in the town and I suspect you'll never get more than about 5% of them going to the club regularly. Good luck to them.
If you live in Henfield, Haywards Heath, East Grinstead etc are you more likely to gravitate to Brighton or Crawley (assuming you're not already a Chelsea/Man U/Liverpool fan watching Sky)? I just don't see Crawley as any kind of threat to our supporter base, even if the unthinkable happened and they got into the Championship and we went down to League 1. I couldn't stand the club in the Majeed/Steve Evans times but these days I just think, good on you, and good luck Richie Barker.
East Grinstead is in the Palace catchment area...