As mentioned previously, application letters and cover letters are not the same. A cover letter identifies an item being sent, the person to whom it is being sent, and the reason for its being sent. A cover letter provides a permanent record of the transmittal for both the writer and the reader.
Nobody liked your project idea, so we are not going to give you any funding. The first version is a weaker statement, emphasizing facts not directly relevant to its point. The second version provides the information in a simple and direct manner. But you don’t need to be an expert on style to know that the first phrasing is diplomatic and respectful (even though it’s less concise) as compared with the second version, which is unnecessarily harsh and likely to provoke a negative reaction.