This form of ownership was created in the early 1900's as a way to get around newly created Federal Anti Discrimination laws. Members of a coop association can arbitrarily refuse to allow a prospective buyer to buy. No reason needs to be given. It was used to discriminate against Blacks, Jews or anyone else the members of a coop did not want to have living in the building. Today coops tend to have very picky (pain in the ass) board members, particularly in NYC, not so much here in Chicago.
This form of ownership prevents 90% of all banks from lending in them because banks must follow Federal Law. As a result of all of this, coops are very unpopular and usually avoided. You can get a good price because values are much lower than condos because no one wants them or no one can get a loan for them. I would avoid them. There are no benefits to coop ownership although they are not that unpopular in Hyde Park Illinois because the U of Chicago helps with financing. Otherwise, stay clear of them.
1. You can meet all the neighbors before you buy. Don't like that nosy loud mouth who can't stop looking at your alternative footwear, just saved yourself a few hundred grand. Creepy guy upstairs from your prospective place, thank him for sparing you future nightmares. Imagine if you could meet your condo neighbors before you purchased, or meet all your new work colleagues. Life might look a lot more like Co-Op living.
2. You will have an opportunity to one day sit on a board and have the power to tell people that they are not worthy. That sounds very exciting.
3. You will always become a talking point at a party when the conversation turns to, "oh, I live in a co-op." "Really? I've always wondered about those. Please, tell me more"
There is nothing wrong with buying one, it's just a preference. Co-ops used to be the only way of owning attached housing before the Great Depression. Then most of them went defunct after the Crash. New York City is probably the most common place in the US to find co-ops. In Chicago, they are mostly found in pre-war buildings along Lake Shore Drive.
Benefits? That depends on what you view as benefits. Co-ops often are more "controlled" as to who they allow to buy in, and who can live there (ie: only the title holder can live there)... they rarely allow renters... they sometimes exclude pets, and they usually require a substantial downpayment.
Due to some of those restrictions, loans are often a bit more difficult to obtain, and due to the higher "entry level" of the downpayment, that often brings in a more financially secure owner. And you'll often get a bigger bang for the buck in a co-op, and sometimes a lower tax burden.
A Co-op is a bit different. One owns shares of the building. The board can let anyone they want and reject anyone at all for any reason. If a person defaults on their property and walks away from it there is no foreclosure, the other owners must take over for the taxes and monthly assessment.