When you choose the fixed price, the developer is under a lot of pressure. As they don’t have full picture of the final product beforehand, they can’t be sure how much time and effort it will take to complete it. That’s why they usually overestimate and you end up paying a lot. What’s more, since the developer is not paid extra for each feature and task that could possibly come up during the development, the work can be rushed and of mediocre quality. You can probably already see the deal isn’t really risk-free for the client. The risk is a potentially subpar project that have lost a chance to be improved on the conceptual level during the development.
 
In most cases, the time and material method undoubtedly makes for a better product. The development team cooperates with you all the way to make the project as great as it could possibly be for your target. The scope of the project can be easily changed without having to modify the agreement. You pay for what you want to pay, prioritize tasks freely and have full access to reports on the development process. The only major shortcoming is that depending on how much time, effort and, well, material will be used, the price will increase accordingly.