(I have avoided including definitions of both and the negatives to save space)
As a sole trader you are the only person of authority in the business. This means that all decisions made are by you, allowing for quick thinking and decision making in business moves. You also have full control over the business meaning that no decisions have to be passed through anyone else before action is made. A sole trader also benefits as they keep all profits from the business operations after all expenses are paid such as rent of property on wages of employees. Being a sole trader is also something that it's generally very easy to set up, only requiring a small amount of capital to get going.
On the other hand, under a partnership all responsibilities are shared, allowing you and your partner/s to focus on your specialist areas, allowing for the best man to partake in a desired job. This further allows for greater diligence to be taken when performing tasks. With more partners it is also likely you will raise more capital, allowing for more flexibility with set-up and running costs. Due to there being more partners involved, consultations can be made between partners on what they think is the best direction to move in for the business, allowing for outsider analysis and a new perspective on a given situation.