It's a natural side-effect of using immutable structures. When you need to modify you allocate a new object with the mutation. This naturally has an impact on the GC because it needs to allocate and recover more garbage.
As an aside, my final year project for my CS degree included benchmarking different sets of SK combinators for efficiency as well as looking at different reduction algorithms.
What I found out pretty quickly is that, especially as I was running my code on a mid 80s mini computer, I had to spend as much time on allocation and garbage collection strategies as anything else. Indeed, my only really "difficult" bug was caused by my premature re-use of application nodes - I thought I was being clever re-using them immediately but it caused problems months later when I started writing recursive expressions using the non-native Y-combinator. I had no idea what was causing the problem and was really quite worried, I was stumped for days and then I had a flash of insight from nowhere while sitting on a bus that fixed the problem.
I remembered that I thought I was being awfully clever re-using application nodes aggressively - turns out this worked fine for non-recursive code or code that used the native Y-combinator in my reduction engine but failed when I used a Y defined directly in the lambda calculus. I removed this "optimization" and the problems went away.
What I always remember is that the idea as to what was causing the problem came as a complete bolt from the blue when I was thinking about something else - perhaps the first time that something like that happened to me, but certainly not the last!
so, no real evidence except anecdotes. Anyway, I was not claiming anything about functional programming being better. I was merely saying Object-Oriented is not necessarily data-centric.
That being said, Lisp & OCaml programmers will argue the statement that FP implies immutability. OCaml strings ARE mutable, (so are OCaml arrays) and you have the keyword 'mutable'. Lisp has setq ...
IMO FP does imply that you treat mutation & side effects with the respect they deserve.