Most exploits tend to be in new code (contrary to popular belief), which in all modern browsers is written in modern C++. The WTF (Blink/WebKit) and the MFBT (Firefox) are state-of-the-art template libraries; you are free to search for those libraries and verify for yourself. New C++11 features such as rvalue references do nothing to avoid memory safety problems; in fact, they make them worse, since "use-after-move" is now a problem whereas it wasn't before.

I know it's hard to believe, but C++ is not memory safe, old C++ or modern C++, in theory or in practice. The new C++ features do effectively nothing to change this. As far as use-after-free goes, C++ basically adds safety over C in two places: (1) reference counting is easier to use and is easier to get right; (2) smart pointers are arguably somewhat less likely to get freed before accessed again due to the destructor rules (though I think (2) may not be true in practice). Browsers have been making use of these two features for a very long time.

Bringing up modern C++ here is "no true Scotsman" unless you can point to a specific C++11 feature that browsers are not using that is a comprehensive solution to the use-after-free vulnerabilities they suffer from. There is no such feature I am aware of.