In writing grants, success for conveying a message, whether it be first or third person, depends on knowing your audience.
Writing formally forces us to write better
in most cases. There is room for both approaches when you truly understand your recipient audience. For federal and state proposals, and for those going to a foundation with multiple staff members and some 'distance' from the funding source, the formal third person should always be used.
For a small local family foundation which is asking for 'letter style' proposals, first person is certainly acceptable, and somewhat preferred over very formal third-party voicing. Yet even in an informal, first party voice, statistics or measurements of success should always be verified by an 'outside source' reference whether it be the local news media or the federal census bureau.
If you sit on the local board of auto-parts dealers reviewing requests for funding, a nicely written first-person voice is going to hold attention far better than something written in formal 'proposalese'.
The biggest problem with first person writing (from a reviewer's viewpoint) is the writer often can get caught up 'inside the story' rather than just telling the story, and completely removes objectivity for the harder questions regarding sustainability, functionality and evaluation. They often fall short of conclusive, justifiable statements or offer proof other than "we think this is wonderful because everyone told us so...".
I recently spoke with the Executive Program Director of a Family Foundation in our area with fairly deep pockets. Although they have a relaxed 'home-town feel' to their website, the Director cautioned me that two former school principals, three bank executives and an English teacher sat on the review committee. Her advice was: "don't waste words, be succinct, tell a compelling story, and make sure your budget is neat, clean and without mistakes".
That advice applies EVERY TIME no matter the approach!