Are the Ivy's really that much better?

I am about to be a sopre at a school ranked approximately 50th in the nation for Liberal Arts colleges. I had a 4.0 in high school with 9 AP 5 scores and a varsity tennis player. I applied to 5 schools, got into 4 but not into Washington University in St. Louis. I got into Northwestern, but my family could not afford it. For some reason, this has really bothered me, even 1 year later. I am very bothered that many of the so called 'top universities' do not let in students like me who went to a racially diverse close to inner city public school. I had 3 other clmates with similar grades and AP scores with the same story. I have a 3.93 in my first year at my school (only non A's were A- in Spanish both semesters). I was wondering what separates those 'top schools' from the rest, and how going to a smaller school affects my chances at top graduate scholarships and schools. I guess a lot of it is an inferiority complex and jealousy, but I really would like to know how much better the schools like Harvard, Yale, Stanford, etc. than smaller schools and how going to a smaller school affects my chances of top scholarships and graduate schools. I would like to go into Engineering (most likely mechanical or civil) and would it be better to go a large prestigious university or a public university?