Typically this is true, but it's certainly possible to get comparable performance with functional style. Carp, which I linked above, basically uses the same approach to memory management as Rust. It doesn't rely on GC.
I also find that for most cases it really doesn't matter all that much unless you're in a specific domain like writing drivers, making a game engine, etc. Computers are plenty fast nowadays, and ergonomics tend to be more important than raw performance.