It's hard for me to say how much it matters, because that would depend a lot on the efficiency of the GC and how many copies are forced (which is a property of the application's data structures).
Even with Clojure's sharing, it is still the case (as I understand it) that you're forced to copy all nodes between the root and any node that actually changed. A mutating approach doesn't have to do any copies; it can just mutate the interior node of the tree.
As an example of a degenerate case, imagine that your root has 10,000 children. If I understand correctly, any mutation to any object in the entire graph requires duplicating the root and the entire 10,000-element array.
I honestly have no idea if this would be an important issue in practice or not, I just wanted to mention it as a super-brief pro/con list of immutable data structures.