* Owning is better for things you use all the time, need immediate access to, and/or plan to keep long-term. It takes more space and money, but it saves you a lot of time and trouble. There are many obvious advantages to owning a home, which most of us use a great deal.
* Sharing or renting is better for things you use occasionally, don't need immediately, or only want to use once. It saves space, money, and resources. The latter is especially important with regard to capital equipment -- compare everyone owning a lawnmower or a complete shop full of handywork tools vs. a cohousing community sharing one or two lawnmowers and a workshop. Fewer resources would be used, at a much lower cost, and more people could use the same stuff at different times. Because you're not duplicating all those purchases, you can then buy more goodies to share. That workshop probably has ten times the tools a single hobbyist could afford.
* Owning is better for things which are precious. Sharing is better when adequate quality is good enough, or when you can't afford an expensive item yourself. Take our workshop example. After trying out the tools, you might decide to buy top-notch versions of your favorites to keep at home. But you probably can't afford the nifty powered hammer everyone chipped in for, nor do you need your own of that.
* Owning is better the more rooted you are. Sharing or renting is better the more mobile you are. So long as you have free choice whether, when, and where to move either is fine. But when people get stuck somewhere they don't want to be, or forcibly torn away from home, that does a lot of harm. Bear in mind that the vast majority of local-Earth is extremely hostile to a genuine traveling lifestyle, and expects people to be settled -- or pretend to be settled for some months between moves. This is a problem in a society that increasingly forces people to move, but does not support their doing so well. That is disrupting the economy as well as lives.
* Owning is better if things make you feel happy and secure. Sharing is better if things make you feel miserable and weighed down. People who prefer to own many things need more space. People who dislike owning too much will be happier in a concise space that discourages clutter -- and gives them an excuse to turn down unwanted bulky gifts or houseguests. This is primarily a matter of personality, and it's less malleable than many other factors discussed here. Consider which way you tend to lean, and make your choices accordingly. Again, forcing people to go against their nature tends to do harm.
* Owning gives you more control over your space and what you put in it. However, if you live with anyone else, you give up some of that control just by sharing your lives. While more people live alone today, it is not very healthy for humans to do so. Living together is healthier for most people, so consider that when deciding what you wish to own.
* Sharing means you have less control. If you share with people who have similar values as yourself, most of the time you'll want the same things. This makes the quality of companionship a crucial factor in the desirability of sharing. Nobody wants to share with people they hate, but most people enjoy the company of friends and family. When people have no choice over who and what they share, it becomes a detriment instead of a boost.
* Many survival needs -- including food, water, shelter, and clothing -- relate to owning and sharing. People need secure access to all of those in reasonable quantity and quality in order to stay healthy and happy. Privacy is also a survival need, although much less recognized as such. Without it, very bad things can happen to civilization as well as personal health. Also, all organisms suffer negative consequences from overcrowding. Cramped living space causes a lot of problems. Minimum standards vary drastically, but here is one example. Note that sharing space expands the type of rooms required, not just the area. It would be better if the 6+ category required at least one more function room, as that is about where people really start needing to split up.
* Whether property is owned or rented, crowding is an essential factor. When too many people try to use the same resource at the same time, its effectiveness drops or disappears. A quiet park is relaxing; a crowded park is not. 10 people can probably share one hammer comfortably; 100 people probably cannot. Ideally, items should get regular use, but have some fault tolerance for swings in demand. Don't max out capacity on anything or every little surge in demand will cause problems. This can help you decide between owning and sharing, and how many of a thing you need.
* Owning is more secure than sharing, to the extent that your storage space is safe from theft or damage. In order to take or tamper with your things, someone must physically get into them, which is very risky behavior. Books on yourself cannot be removed or altered at the whim of a library service. Sharing is more secure than owning, if your personal space is not very safe. Things stored in the cloud cannot be lost if your junkie roommate steals your computer; you can simply access your data from a different device (even at a library, until you buy a new one). Different types of security therefore exert strong influence over people's choice between owning vs. sharing. A city without bike racks is a poor place to own a bike; one with bike racks is okay; one with bike garages is quite secure. But a citywide fleet of day-glow orange public bicycles doesn't really need garages to lock them in.
* Due to conservation of resources, sharing often means you have the use of a great deal more than you could afford to own. Take a look at this community. It has modest-sized housing units packed closely together. That leaves a lot of space for gardens, a gazebo, a community center, a playground, a badminton court, a jogging track, and so on. If they had instead divided the land equally, each would have a private yard but none of the communal amenities; even if they had a neighborhood park, it would be a considerable distance from most homes. By sharing, each person gets to use any of that common space within immediate walking distance. Because they have chosen to build very diverse facilities, this reduces the tendency of people to crowd into one spot and instead spreads them out in groups according to different interests. It also balances small private homes against expansive public features.
* Successful sharing relies on products designed for sharing. For example, toys and tools for school use must withstand the wear and tear of many small hands, and the same applies to a household with lots of kids. Montessori tools cost a lot more than grocery store toys because they are made from beautiful, quality materials and last for years. Now consider living space. The more people share a home, the more space they need -- not just private space, but different communal spaces too. Compare and contrast the following examples ...
This apartment is badly designed for a shared household and not much better for a family. There are two common bathrooms, so nobody has a private one, and no bathtub. All of the common space is crunched into the middle, so you have to walk around things to get anywhere and there's no way to divide activities. Even four people would feel crowded in this space, let alone more.
This apartment is perfect for 4-8 people sharing a household. Each bedroom has a private bathroom, plus a common powder room on the second floor. The ground floor includes a 2-car garage, four storage units, and a rec room for noisy activities. (That could just as easily be a music room, craft room, kids' playroom, exercise room, etc.) The second floor has a dining room, kitchen, living room, powder room, and one bedroom with ensuite and walk-in closet. The third floor has three bedrooms, each with ensuite and walk-in closet, plus a laundry room. Everyone has adequate privacy and storage space, along with enough communal space to congregate or break into smaller groups as desired. A further advantage is that the walk-in closet may be converted into some other purpose such as a kitchenette, quiet corner, office niche, or nursery.
In the first apartment, the cramped quarters offer minimal improvement over four studio apartments. But in the second, each person gets access to a LOT more space and different types of equipment compared to apartments, yet the 4-bedroom 3-story home takes up much less room than four separate houses would. So long as family members or other housemates like each other, sharing the 3-story home offers many more benefits than living alone. The cramped apartment is probably a poor trade, and unless they're extremely attached to each other, they'd probably be better off in studios. So you can see that how well sharing works will depend a lot on the context.
That means infrastructure has a huge influence on the effectiveness of owning vs. sharing -- and in local-America, what we have isn't often what we need either to buy or to share today. Much of it is out of step with consumer needs, either because it's carried over from earlier times or poorly designed because people didn't do their homework.
Choose mindfully, and consider these factors when voting on housing-related issues in your area.