Well my sorority has been around since 1989 and we are definitely still going strong. The national sororities are the one's that are struggling because they're always worried about getting numbers, being put on probation, or getting their charter revoked.
We don't have to worry about numbers. Recently a national sorority purposely had their charter revoked because they didn't like the rules and went local. They are now completely gone. One of the last remaining members of their sorority disaffiliated herself with them and joined my sorority.
I would say there isn't a lot of competition on the campus that I went to school at. I wouldn't exactly say that the nationals have an advantage over us because we usually do better than them during recruitment. We usually take between 45-50% of the girls during rush. The nationals get more girls through COB. We usually don't COB unless we really know someone well.
Have a nice day