Conceptually they are similar, though it's always important to note that C++ has several man-centuries worth of compiler work. Rust may become stable and efficient enough to replace some existing C++, but at the moment it's most certainly not as mature as the existing C++ ecosystem.
Rust uses LLVM, so it benefits from the same optimizer as clang. The front-end is less mature of course, but also Rust is less complex, so may not need man-centuries of work to be parsed properly ;)
Currently Rust doesn't outperform C++ partly because LLVM is optimized for the C subset (can't take advantage of extra aliasing/immutability information Rust has), but given that Apple is now betting on (quite similar) Swift I expect LLVM to rapidly improve in this area.
Also remember most of the work on Rust at the moment is focused on stabilizing the language — performance is only really required to be acceptable for now, provided it is possible to improve.
Yes, there are several places where, for example, we generate sub-optimal LLVM IR, but time is better spent getting the interfaces and language spec correct for 1.0 than squeezing out performance.
I should mention that that's different than 'who cares about performance, let's toss this in.' Performance aspects are absolutely taken into account when changing the language. But that's different than the implementation itself.
