I'm not going to claim that we have proof the Rust is more productive than Go or C++. I see some concrete advantages, however, Rust may simply better suited to the work we're doing. We might just enjoy writing it and therefore work faster.
The way I see it is that Rust guides you to better architectures, it offers a lot of very powerful features from FP and PL theory, and it's all engineered to make sense as a language. In that way, I think it's similar to Go in that they're both engineered while C++ has a lot of fossilized layers and has been organically grown for decades now. We have C++ code from half a decade ago that looks nothing like what we are writing now. It's this organic beast that has a lot of baggage. Rust and Go are engineered from the ground up, and with Rust editions I think they will avoid becoming the organic beast that C++ is now.
Similarly, the productivity difference will depend on how much run-time performance you need. It might be take longer to make Go code very fast if you need very fast. Having to work around the garbage collector, and avoiding interface {} etc.
well, Rust code from half a decade ago is also somewhat distinct from today's rust.. even basic cases don't compile anymore : http://progopedia.com/language/rust/