I think Zig would be much easier to write code for compared to Rust in this use case. Rust is not some magical tool that stops all bugs as some people like to think it is. The lower you go, the more you will have to contort yourself, and the more likely it is for less experienced programmers to make mistake. I think Zig is much more approachable and fixes a lot of C foot guns and guides you into writing safer, faster code.
If you are writing web apps then Rust is probably "safer". If you are writing low level code that requires obtuse memory management then I don't think you can make a blanket claim that Rust is just "safer". A lot of this nuance is not often discussed.
Does Rust offer many advantages over Zig in this space?
I mostly program in C, but I've been eyeballing both for some time now.