It's unfortunate that they're often talked about as comparable things (as Go vs Rust) because they're totally fundamentally different languages, including what spaces they target.
I think part of this is due to Google initially trying to position Go as a systems programming language and sorta like an easier C.
In reality, Go is so far distant from C or C++ that it would be better to describe it as Java related honestly.
The real question is what do you want to do or why do you want to learn.
Do you want:
* Something where you can quickly produce working code
* Something with a large, complex, and questionable quality ecosystem (as ruby/python have, but a smaller scale)
* Something that's pragmatic, but not elegant
* Something that's well suited for writing a webserver, cli tools, or daemon
* An ecosystem of people who do not like complicated languages and rarely talk about complex language-theory concept
* Something that fills a similar role to python, ruby, java
* Something that has a massive foothold in the docker/container ecosystem
* A language driven by a semi-opaque "open source" process with a big company and closed doors at times
* Really easy to use concurrency (but also easy to shoot yourself with)
* Nice editor integration, autocompletion, etc.
Well, Go wouldn't be bad to learn
Do you want:
* Something where you'll actually learn new concepts, ideas, and be challenged in some ways
* A fledgeling library ecosystem where the libs that exist are decent quality, but most just don't exist
* Lots of opportunities to contribute
* A community-driven project where your opinion can make real changes happen
* A powerful macro system
* Actual type safety! With real algebraic types!
* No GC pauses
* Elegant error handling and abstraction powers
* Something it's hard to write working code in, but once it compiles it's probably pretty good
* Something great for writing an OS or low level tools in, and mediocre for webserver, cli, etc currently
* Something to replace C++, possibly D, possibly ocaml
* A language that is technically an ML but doesn't feel like one
* A super-smart community willing to talk about some of the coolest topics in language design and CS
Rust could fit for you
Grain of salt, I write lots of Go and am working on getting to know rust better still.
To all the people saying "Go is used professionally, rust isn't, don't learn rust from career perspective"... there's another axis!
You also have to consider what skills you'll pick up with each. Learning Rust will improve your ability to write safe C++ and help you reason about some types of problems in all other languages, so even though rust itself isn't directly marketable, the skills you get will be helpful regardless.
Learning Go will help you reason about actors a little and some problems in other languages, but not nearly as many and, frankly, the community for Rust will teach you a lot more about everything.