There are important differences between a Partnership Agreement and a Shareholders Agreement
The first and most important difference is that the partiers in a Partnership are all personally liable for the debts of the Partnership. This is the main reason why people often choose to rather start a new company. However, you are free to do so at a later stage.
On the upside, a Partnership doesn't require a formal registration process. Once the partners have signed the Partnership Agreement, the partnership has been formed. It is immediate.