If you do hand optimize your code, all bets are off. With both languages. But I think the notion that the Rust compiler has more context for optimizing than the C compiler is maybe not as controversial as the notion that language X is better/faster than language Y. Ultimately, producing fast/optimal code in C kind of is the whole point of C. And there aren't really any hacks you can do in C that you can't do in Rust, or vice versa. So, it would be hard to make the case that Rust is slower than C or the other way around.
However, there have been a few rewrites of popular unix tools in Rust that benchmark a bit faster than their C equivalents. Could those be optimized in C. Probably; but they just haven't. But there is a case there of arguing that maybe Rust code is a bit easier to make fast than C code.
Well, then in many cases we are talking about LLVM vs LLVM.
> Ultimately, producing fast/optimal code in C kind of is the whole point of C
Mostly a nitpick, but I'm not convinced that's true. The performance queen has been traditionally C++. In C projects it's not rare to see very suboptimal design choices mandated by the language's very low expressivity (e.g. no multi-threading, sticking to an easier data structure, etc).
Compiler optimisations certainly play a large role, but they're not the only thing. Tracing-moving garbage collectors can trade off CPU usage for memory footprint and allow you to shift costs between them, so depending on the relative cost of CPU and RAM, you could gain speed (throughput) in exchange for RAM at a favourable price.
Arenas also offer a similar tradeoff knob, but they come with a higher development/evolution price tag.
I'd say most people use this definition, with the caveat that there's no official "average programmer", and everyone has different standards.
If you prefer it, salaries correlate with years of experience, and the latter surely correlates with skills, right?
(No, this doesn't mean that every 10 years XP dev is better than a 3 years XP one, but it's definitely a strong correlation)
In that context, the designer can reason about how should code written that way should perform.
So I think this is a meaningful question for a langauge designer, which makes it a meaningful question for the users as well, when phrased like this:
'How does idiomatic code (as imagined by the language creators) perform in language X vs Y?'