Are there peer-reviewed papers studying the pros and cons of functional programming?
There is a famous paper "Why Functional Programming Matters" by John Hughes. The main argument of this paper is the modularity of functional programs.

Also, the work by Chris Okasaki about functional data structures is very interesting. The article "Red-Black Trees in a Functional Setting" provides a very clear implementation of red-black trees using functional programming language, which is much simpler than their imperative implementation in the book "Introduction to Algorithms" by Tomas H. Cormen et al.