The letter on the left is fake. It did appear in an official Doctor Who publication, but it was not written by Peter Capaldi at the age of 6. It was a gag letter included in the 1963 facsimile edition of Doctor Who Magazine included with the 50th Anniversary issue.
There was no Doctor Who magazine in 1963 for Peter Capaldi to write to. The first issue was published in 1979.
The letter on the right, WAS written by Peter Capaldi, and published in RADIO TIMES (Not Doctor Who Magazine, as it still didn’t exist) in 1974, when he was aged 15.
Hope that clears things up.