Public schools tend to give a lot of "need-based" scholarships, aka "we'll charge you whatever you can afford". Private universities are more open to "merit-based" scholarships on top of that, where they're actively trying to attract top applicants by reducing their effective cost, oftentimes to even cheaper than public universities.
As a result, if you're from a low-income background, but overcome the odds and manage to be an academically competitive applicant, most private schools will be offering something close to a full-ride once both need and merit based scholarships are considered.
As a result, if you're from a low-income background, but overcome the odds and manage to be an academically competitive applicant, most private schools will be offering something close to a full-ride once both need and merit based scholarships are considered.