This 'question' is bound to go up in flamewars, but here is an honest and unbiased answer by someone who has taken a look at nearly every language on the planet (a hobby) and thinks that both languages are a bit crappy from a general programming language perspective but quite usable in practice.

Go is good to get things done quickly. It has a vast ecosystem and super-fast compilation. It's like a modern BASIC, but more performant and fun to use. It's fast enough for most everyday tasks except for real-time audio processing and high end gaming. It's good for writing CLI tools and server backend software.

Rust is good for writing libraries and CLI tools that replace existing C or C++ solutions with inherently safer versions and when speed matters a lot, though not as much as what would make you use Fortran or hand-optimized C. It is not suitable for high integrity systems and solid engineering where you'd normally use Ada/Spark, because of low maintainability, an unprofessional 'language aficionado' user base converted from C++, and being a fast moving target. Maybe later, though.