LetterCounts[str, 2]
and
KeyMap[FromCharacterCode,
Sort[Counts[Partition[ToCharacterCode[str], 2, 1]], Greater]];
are not equivalent operations - just try the inputs found in the LetterCounts documentation and you'll quickly see differences. So the timing comparison is not very meaningful.
edit: To answer the question in the comments, the self-written
myCharacterCounts[str_, n_] := KeyMap[FromCharacterCode,
Counts @ Partition[ToCharacterCode @ str, n, 1]
]
will run slightly faster than CharacterCounts[str, n], though on my machine the difference is sub-millisecond even for very large strings.
But this myCharacterCounts function still does not do everything that CharacterCounts does.
CharacterCounts takes options, as in
In[45]:= CharacterCounts["aAbBcC", IgnoreCase -> True]
Out[45]= <|"c" -> 2, "b" -> 2, "a" -> 2|>
and does argument checking, issuing a message for CharacterCounts[] or CharacterCounts[2]. Argument checking and options handling are generally required for any built-in system function, but not needed for self-written functions where you know you won't be passing bad arguments or options. This may be enough to account for the timing difference, or maybe CharacterCounts is being inefficient somewhere - I can't say.
I will say that it is often, but not always, possible to beat the timing for built-in functions if you focus on a subset of the functionality and neglect error handling. And if your application is time sensitive then it is worthwhile to use the custom function instead.