It would likely have LESS memory corruption problems, as you're eliminating places in the code that that can occur. The real question is: Does Rust allow you to write less bugs? That's a somewhat open question, but it definitely eliminates certain classes of bugs which are common today.
From intensive but still hobby usage for the past 10+ months I get a feeling that I have a lot /less/ bugs, and if I do have one it is an algorithmical error rather than some UB.
This is of course just my view and is heavily skewed towards what I usually do, which is Games and Web Apps. It also depends on how you qualify a bug. (Is a panic a bug? Might or might not be.)
To continue that train of thought: I have a feeling Rust will change what one would consider a bug (inside the Rust ecosystem at least). Since you do not actually corrupt memory most of the time (minus unsafe shenanigans) you actually do not get a lot of cases where you get a crash and you don't know why. RUST_BACKTRACE always told me where something panicked which is pretty much always sufficient to debug since you just have to verify your invariants you thought were correct when you for example 'unwrap' or call panic! yourself.
