One big advantage is that this unified recursive representation of code allows structural editing. With things like Emacs's paredit you manipulate code structure directly by splitting, joining, and moving subexpressions instead of editing code as flat lines of characters.

Btw, of modern Lisp dialects, I do not like Clojure for undermining this advantage by not syntactically grouping everything that is grouped semantically (e.g. binding pairs in let) just to use less parentheses. In my opinion, Scheme syntax (Guile is a Scheme implementation) is much better.