They are both in the public domain....but, for very different reasons.
Copyright protection extends to the author of the work at the moment of creation. In this case, however, Mr. Slater did not take the picture. The monkey did. So, who owns the copyright, the monkey? No. Sadly for this beautiful monkey, copyright regulations are clear that works created by animals are not eligible for copyright protection. Alas, this picture was in the public domain the moment it was taken and can be freely copied and distributed and posted on blogs that talk about the copyright protection of the character, Sherlock Holmes.
That issue is now on its way to the U.S. Supreme Court (if they decide to accept the case). Judge Posner, writing for the 7th Circuit, in an opinion published August 4th, rejected the argument by Doyle's estate that the character of Sherlock Holmes continued to evolve and become more complex throughout Doyle's series and, therefore, the character itself is protected by copyright until 95 years after publication of the last story in 1927 (so protection would last until 2022). Rather, Judge Posner said, "[w]hen a story falls into the public domain, story elements - including characters covered by the expired copyrights - become fair game for follow on authors. There is no ground known to American law for extending copyright protection beyond the limits fixed by Congress."
So, unless the Supreme Court picks up this case and finds some unprecedented reason to extend the copyright life of Holmes, it seems the character is "fair game for follow on authors" and the Doyle estate ends up looking like a mon....well, looking silly.