In general, in a place where land cost is very expensive, the builder build coop, so you see many prestigious location in Manhattan you can only buy coops. One reason, I guess, is because the original owner(s) or company wanted to have control of the future appreciation, also, the initial cost is lower. That is you may be able to build more.
Of course, if the land cost is so high, you see builder would rather build hotel.
Coop is kind of between apartment and condos, ownership wise, however, the "physical shapes" they are all similar except for the same grade of the 3, apartment tends to be smaller and condo bigger with coop in between due to the fact tenant often stay shorter than condo owner.
Owning a coop is like renting an apartment with OPEN END lease, not renew every year. If you need to renew every year, you will cry like my friend at Avelon Cove Jersey City NJ called me his rent jump $300 a month. Do you want to move out or renew? So, ownership is very important. There is many New Yorkers eventually fight with landlord because they made a wrong decision to stay at rental apartment for many years, 10 or 20 years!!! They should just buy a coop.
For condo, you got many of yours such as your a/c, furnance, hot water heater ...etc because physically you almost do not share these facilities, but you may still share parking lots, garbage, lawn maintenance, snow removal ...etc.
After knowing the nature of coop and condo, you also need to understand "purchase" involves money, and at rising market, coop seems to move up MORE than condo percent wise, on the other hand, coop will also move down more than condo, but there are exceptions as well.
Coop has the potential that it may be converted to condo at rising market, and when that happen, your coop value may be double overnight.
In the good old days, people also decided to buy coops if they do not have enough downpayment to buy condo which is usually twice the price of similar coop. Of course, if people has only security deposit, they would just have to rent an apartment. So the rule of thumb is that if you do not have or do not want to tie up your cash flow, you either rent or just buy a coop.
You may have seen many empty nesters sold their big house and downsize to a coop. Why not just rent? As mentioned above, when you rent, you are under a risk to have rent hike, but people retired with kids bought their own home, they still need a permanent place to called home, so coop seems to be a choice. For one reason coop over condo for the retired is that it is like living in a rental, not much to take care.