All schools use the same formula and give about the same aid. Aid packages vary considerably, the biggest differences showing up in the distribution of institutional grants in private colleges. Federal financial aid is awarded on more or less the same basis from school to school because the awards result from the Federal Methodology calculation which Congress developed. Congress makes substantive changes to the formula every five years and cost-of living adjustments annually. All colleges use the Federal Methodology in calculating a student's Stafford Loan eligibility, for example.
Federal aid is very similar from school to school.
Aid packages at private colleges vary because the Federal Methodology does not restrict they dispense their own money. Even though institutional methodologies do vary from college to college, they track the Federal Methodology closely. In making decisions about disbursing their own money, most private colleges do count home equity. The house doesn't count. See Myth 5.