There's one important difference. As far as I know, the bounds checking of gcc or clang can either print a warning and continue, or terminate the process.

A panic in Rust, however, will safely unwind the stack (similar to a C++ exception, in fact it's the same mechanism) and terminate only the thread. The rest of the program can continue running, and even start a new thread to replace the terminated one.

You can see this in action when running "cargo test". A panic in a test (the assert!() and assert_eq!() macros, often used in tests, do a panic in case of failure) will not terminate the whole process; the rest of the tests still run.