I co-owned a horse with Lisa of Ruff N Tuff Miniatures here on the forum. Since I know her, and know her program, and know how she cares for and treats her horses, I had no fears about co-owning with her.
Co-owning a stallion (I would never co-own a mare or gelding, there really is no point) is generally good if each partner has something specific they want from the stallion (such as breedings) and both partners agree it will work out. It definitely allows you to purchase a horse more expensive than you might be able to otherwise afford.
However, if this is the case, also consider breeding to outside stallions, as this might be cheapest in the long run. If you have a really super mare and can breed to a really super stallion, you might get a super colt that you can retain for a stallion down the road. This is what breeders of really expensive breeds tend to do, as stud fees are never as expensive as buying a really nice stallion... it's only a fraction of the cost.
You also need a VERY thorough contract. Think of any and all fees related to said horse, and who is responsible for it. Think of any and all situations that can arise with the horse, and put stipulations in your contract that will cover and protect it.
Good luck with whatever you decide,
Andrea