The press release from Nagin's office regarding those who were to be sheltered at the Superdome was that the site was meant for those with "special needs" with 1 caretaker allowed to accompany that individual, it was to be a refuge of last resort and that those seeking shelter there (SD) should bring food and water to last 5 days.
And the people who ended up at the Convention Center were the people who LEFT the SuperDome when they found out the buses were going to Houston.