The two different approaches have names: Lisp-1 and Lisp-2. A Lisp-1 has a single namespace for both variables and functions (as in Scheme) while a Lisp-2 has separate namespaces for variables and functions (as in Common Lisp). I mention this because you may not be aware of the terminology since you didn’t refer to it in your question.
Wikipedia refers to this debate:
Whether a separate namespace for functions is an advantage is a source of contention in the Lisp community. It is usually referred to as the Lisp-1 vs. Lisp-2 debate. Lisp-1 refers to Scheme’s model and Lisp-2 refers to Common Lisp’s model. These names were coined in a 1988 paper by Richard P. Gabriel and Kent Pitman, which extensively compares the two approaches.
Gabriel and Pitman’s paper titled Technical Issues of Separation in Function Cells and Value Cells addresses this very issue.