I strongly favour CVs and applications written in the first person as this lends itself to a more modern and succinct style. CVs written in the third person tend to obscure the content of the CV and make it difficult for a reader to isolate your individual skills and achievements.
Recruitment agents in particular need to cut through to the core facts quickly; making their job difficult does not endear you to them. On a practical note, the third person style is generally reserved for applications submitted uninvited by recruitment agents to employers. When I have reviewed applications for my firm, I delete uninvited applications immediately or mark them "return to sender". By writing in the third person, you risk being accidentally binned.
So, whether you're applying direct or going through an agency, writing in the third person is not a good idea. Personally, I find applications written in the third person start off sounding pretentious; sustained over two pages, it starts to sound as if the applicant has a psychological problem.