Rust vs Clojure
Before Rust, I spent years doing clj/cljs development, and Rust feels "more functional" than Clojure in the following sense:
I like Rust's pattern matching more than Clojure's destructuring.
Clojure doesn't have TCO either.
I actually am more comfortable building higher order functions in Rust due to type checking. Clojure certainly has nicer syntax for writing functions that take functions as args and returns functions, but I'm scared to use them for anything complicated.
Rust vs ML
I'm not convinced Rust's FP plateaus before reaching ML level. Better pattern matching + tuple assignment + currying + some macros for faking TCO goes a long way.
Rust vs GC
I could be wrong on this -- I believe versions of Mathematica and variants of APL use RC rather than GC -- and both feel very very functional.
I'm not convinced that GC is a fundamental requirement for Functional style programming.
FP often starts with "mathematical definition" then asks "can we make this def recursive .. and executable", and for this, GC certainly makes things easier, but I'm not convinced it requires GC.
In particular, in a 100% pure language, we should be able to do everything with GC, because without mutations, objects form a "DAG"  because they can only refer to earlier objects.
 There are mutual recursive functions, but in those cases, we can rewrite it as a single function that takes a variant as an arg.