Well, first off, it's not a condo. With a condo, an owner legally owns their unit and it is registered in the land titles system the same as any other piece of property you might buy. The rest of the property (hallways, elevator, etc, in an apartment condo) is called "common element" and is owned and taken care of by the condominium corporation. As a condo owner with share in that corporation, all the 'common element' is essentially owned together by all the owners, and maintenance is paid for through the monthly fees.
Co-ops are an earlier community-ownership option that predates the laws that allowed the development of condominiums and the registration of condo unit ownership in land titles. In a co-op, the entire property is owned by the co-op corporation and an owner owns SHARES in that corporation - not the physical property itself - which allow use of the unit as part of those shares' rights.
Otherwise, co-ops operate on a day-to-day basis in a similar fashion to condos. There is a board of directors responsible for the management and maintenance, and monthly fees that pay for that. Legal requirements around management of co-ops are not quite the same: management may be done almost entirely by the co-op board of directors, whereas a condo should have a professional and licensed condominium management company. This means that quality of management can easily vary from building to building. But, as long as management is well-run, this is not a significant concern.
One of the biggest practical differences from a real estate market perspective is that the type of ownership greatly affects the financing that is available. Because you are not buying a property that will be registered in the land title system, you will not be able to get a mortgage when buying a co-op. Yes, you read that correctly, no mortgage.
There are some financial institutions that will offer financing in a share purchase agreement format, but the amount you can get will be significantly less. With the one I am familiar with, you can only get 40% loan-to-value. This means if you buy a co-op at $300,000, your loan will only be $120,000 maximum. You have to come up with the other $180,000 yourself. With a condominium and a mortgage, you can usually get at least 80% loan-to-value (depending on income qualification, appraisal, etc, of course).
The other option for buying a co-op is all cash, whether your own savings or borrowed from somewhere else like a line of credit or family member.
Some other factors that are important to understand about co-ops is that the shares bring a right to occupancy in a specific unit, but those rights are not unlimited.
For one thing, many co-ops require approval of a new buyer by the co-op board. In theory, this shouldn't be a problem if the buyers are financially stable enough to buy the co-op, but it is at least a step in the sale process that needs to be taken care of.
Another important factor is that occupancy is granted to the owner who owns the shares and their family, and no one else. So in general, co-op units can not be rented out to anyone else. This obviously reduces the market interest in it compared to condominium ownership, as most condo can be rented fairly easily.
The combination of the factors above generally translates into a lower market price for a co-op compared to an otherwise similar condominium. When it's easier to finance and easier to rent, higher prices are more feasible for condos. There is more demand for a condo simply because there are more buyers qualified with the easier financing. However, if you are going to be a largely cash buyer anyways, a co-op might give you more bang for you buck, and possibly less competition depending on the market.
As always, make sure you're working with professionals and do your due diligence. With that, a co-op just might be the right fit for your needs.