It is established etiquette by the Joint Chiefs of Staff, United States Department of Defense, the U.S. Army, the U.S. Navy, and the U.S. Air Force that the closing “Respectfully yours” be reserved for the President of the United States (according to U.S. Army standards, this also extends to the first lady and the President_elect).
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.