Fixed rate is a single price which incorporates all the costs (materials, labor, overhead) and profit. Costs plus has two prices: the estimate base cost (material, labor, overhead) and has the profit as a separate price and additional fee.
The buyer can incorporate high-end materials because the contractor has no incentive to cut material costs. However, the difficulty with costs plus contracts is the level of detail needed in the price calculations in the contract. The indirect costs and overhead should be thoroughly detailed as well. Another issue is that the buyer will not know the final cost of the project until the construction is completed. If this is a concern, a cost-control clause can be added to protect the buyer from exorbitant costs.
The buyer could still end up paying additional amounts if change orders are needed. Typically, the buyer ends up paying more under a fixed rate contract to ensure the contractor will have some profit. One disadvantage to the fixed rate contract is that there’s a perception the contractor will not be motivated to work on your project and buy subpar materials if it looks like the project will be over budget. Whether a costs plus or fixed rate contract is best for you depends on a number of variables including how the buyer is about the budget, and how much detail the buyer knows about the project.