They were originally a segregation tool, which is a bad way to start. It was not uncommon for the government to use imminent domain to evict huge groups of black people to build white-only public housing. That continued up until the early 60s.

The American style of public housing is also often large developments with many occupants. As the occupants basically have to be poor to qualify, the concentration of poverty tends to lead to a lot of negative externalities. "The projects" are often notorious for gangs, drugs and crime. My impression is that much of Europe does more interspersed public housing, similar to Section 8 (subsidized rent to a private landlord) except the government owns the homes. The US attempted to make some strides by redeveloping former "projects" into mixed-income developments, but there is no requirement that the new development have at least as many low-income units as the demolished building. As a result, only about 12% of people relocated from those buildings eventually move back into the new building.

Funding has also been a big issue. The housing developments become delapidated because we don't fund them enough to maintain them. That above mentioned redevelopment project was aimed at fixing the most distressed housing projects; sadly the public housing that was targeted was that which would bring the most money to the city, rather than the most damaged housing. Some have levied criticisms that public housing has been intentionally underfunded so that it seems like a debacle to build support for Section 8, which allows private companies to profit from housing the poor.

Also as a result of the lack of funding, public housing is often hard to get. The median time on a waiting list for public housing is 9 months. 25% of people spent at least a year and a half on the wait list. Housing Choice Vouchers (I think that's Section 8) is even worse; the median time on waiting lists is 1.5 years, and 25% of applicants spent at least 3 years on the waiting list. Over 50% of HCV waiting lists are currently closed to new applicants because they're so backlogged. This is often a compounding issue for people with mental health issues or drug addiction. If you are removed from your unit for any reason, you go to the back of the wait-list. I know a social worker who will fight tooth and nail to get someone with a debilitating mental illness housing, only to have them get evicted the next month as a result of their mental illness.

Lastly, because we build these giant complexes, it's trivial to tell whether an address is an a public housing project. They're not well regarded publicly because of aforementioned negative externalities, so anything that requires an address requires you to basically announce that you live in public housing. That invites a lot of discrimination, especially with job applications and finding housing once you're on your feet enough to try to move out. "Im currently or was recently too poor to afford rent" isn't something that most landlords or employers look kindly on, especially since many in the US consider poverty to be a character flaw.

So historically, US public housing has been racist, in poor shape, hard to get and generally unfavorably viewed by the populace causing discrimination. They're often referred to as "housing of last resort" because they're so undesirable that people won't live there unless they have no other choice. It's effectively the tier directly above living in a tent on the street.