One difference is that it's an incredibly hard problem to check whether your C code is memory safe since every single line of your code is a risk. On the other hand, it's easy to at least assess where your supply vulnerabilities lie (read Cargo.toml), and you can enforce your policy of choice (e.g. whitelist a few specific dependencies only, vendor them, etc).

I would argue that almost all major rust projects use dependencies. Checking the dependencies for vulnerabilities might be just as difficult as checking C code for memory safety, maybe even worse, because dependencies have dependencies and the amount of code to be checked can easily sky rocket. The problem gets even worse if you consider that not all rust code is safe, and that C libraries can be included and so on