Why is $(...) preferred over `...` (backticks)?

For several reasons:

Inside $(), there are no such surprises.

Backslashes are no more no less surprising than elsewhere IMHO

  echo `echo \a` # prints a
  echo `echo \\a` # prints a
  echo `echo \\\a` # prints \a
  echo `echo \\\\a` # prints \a
  echo $(echo \a)  #prints a
  echo $(echo \\a) prints \a
  echo $(echo \\\a) prints \a
  echo $(echo \\\\a) prints \\a

the same sort of things happens without any quotes or within "".

I suspect the real advantage of $( ) here is that you don't need to take extra care of the quotes (\ ""), you just put them as usual, ie echo "echo \"foo    bar\"" vs echo "$( echo "foo bar")" -- pgas

The only time backticks are preferred is when writing code for the oldest Bourne shells, which do not know about $().