Your financial aid is mostly based on income. It is set up so that you cannot receive more than what they have calculated as your "cost of attendance". However, the only students that normally have more financial aid then they need are going to be the ones that also have scholarships and not just federal aid.
Assuming you do not have a scholarship, your federal aid will be the same no matter where you go to school. You will not get more simply for going to a more expensive school. The maximum amounts of grant and loan money are set in stone. They will be the same whether your school costs $5,000/year or $50,000/year.