I wouldn't put it that way. Both languages are fast at nice straight-line code.
The main area I'd expect to see performance benefits for rust (though I don't have experience here) is larger rust programs. Rust's zero-cost abstractions have more benefits as the abstractions nest more deeply. For a small program, you don't really have a lot of abstractions, so Go will do just fine.
I think Go has a number of nice performance tricks up it's sleeve, though, so I wouldn't rule out Go on performance grounds too quickly.
With Rust, you have much more control, but you also need a deep understanding of the language to get the most out of it. With Go, the way you think it should work is usually is Good Enough™.