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.
When you know the recipient’s name, sign it “Sincerely yours” or just “Sincerely”, or in the US “Yours truly” is acceptable. Don’t try anything more cutesy or friendly unless a) you know the recipient quite well and are certain you can be informal without seeming disrespectful, or b) you have a “trademark” letter ending that’s part of your public persona (and the talent and popularity to pull it off). Signature and printed name: Signing your name is a minimal assurance that you stand behind what was written.